At first glance, that might be hard to answer. You won’t find the word “heresy” in your Bible very often.
Unless, you have the King James Version; there, you will find it in Acts 24:14. There it’s used to describe what the pagans called “The Way” – Christianity.
Peter uses its plural, once, to warn:
But there were also false prophets among the people, just as there will be false teachers among you. They will secretly introduce destructive heresies, even denying the sovereign Lord who bought them—bringing swift destruction on themselves. ~ 2 Peter 2:1
There are, however, plenty of false teachings and descriptions of false teachers and what they do outlined in New Testament scripture:
I urge you, brothers and sisters, to watch out for those who cause divisions and put obstacles in your way that are contrary to the teaching you have learned. Keep away from them. For such people are not serving our Lord Christ, but their own appetites. By smooth talk and flattery they deceive the minds of naive people. Everyone has heard about your obedience, so I rejoice because of you; but I want you to be wise about what is good, and innocent about what is evil. ~ Romans 16:17-19
See to it that no one takes you captive through hollow and deceptive philosophy, which depends on human tradition and the elemental spiritual forces of this world rather than on Christ. . . . Therefore do not let anyone judge you by what you eat or drink, or with regard to a religious festival, a New Moon celebration or a Sabbath day. These are a shadow of the things that were to come; the reality, however, is found in Christ. Do not let anyone who delights in false humility and the worship of angels disqualify you. Such a person also goes into great detail about what they have seen; they are puffed up with idle notions by their unspiritual mind. They have lost connection with the head, from whom the whole body, supported and held together by its ligaments and sinews, grows as God causes it to grow.
Since you died with Christ to the elemental spiritual forces of this world, why, as though you still belonged to the world, do you submit to its rules: “Do not handle! Do not taste! Do not touch!”? These rules, which have to do with things that are all destined to perish with use, are based on merely human commands and teachings. Such regulations indeed have an appearance of wisdom, with their self-imposed worship, their false humility and their harsh treatment of the body, but they lack any value in restraining sensual indulgence. ~ Colossians 2:8, 16-23
Concerning the coming of our Lord Jesus Christ and our being gathered to him, we ask you, brothers and sisters, not to become easily unsettled or alarmed by the teaching allegedly from us—whether by a prophecy or by word of mouth or by letter—asserting that the day of the Lord has already come. ~ 2 Thessalonians 2:1-2
As I urged you when I went into Macedonia, stay there in Ephesus so that you may command certain people not to teach false doctrines any longer or to devote themselves to myths and endless genealogies. Such things promote controversial speculations rather than advancing God’s work—which is by faith. The goal of this command is love, which comes from a pure heart and a good conscience and a sincere faith. Some have departed from these and have turned to meaningless talk. They want to be teachers of the law, but they do not know what they are talking about or what they so confidently affirm.
The Spirit clearly says that in later times some will abandon the faith and follow deceiving spirits and things taught by demons. Such teachings come through hypocritical liars, whose consciences have been seared as with a hot iron. They forbid people to marry and order them to abstain from certain foods, which God created to be received with thanksgiving by those who believe and who know the truth. For everything God created is good, and nothing is to be rejected if it is received with thanksgiving, because it is consecrated by the word of God and prayer. ~ 1 Timothy 4:1-5
If anyone teaches otherwise and does not agree to the sound instruction of our Lord Jesus Christ and to godly teaching, they are conceited and understand nothing. They have an unhealthy interest in controversies and quarrels about words that result in envy, strife, malicious talk, evil suspicions and constant friction between people of corrupt mind, who have been robbed of the truth and who think that godliness is a means to financial gain. ~ 1 Timothy 6:3-5
Keep reminding God’s people of these things. Warn them before God against quarreling about words; it is of no value, and only ruins those who listen. Do your best to present yourself to God as one approved, a worker who does not need to be ashamed and who correctly handles the word of truth. Avoid godless chatter, because those who indulge in it will become more and more ungodly. Their teaching will spread like gangrene. Among them are Hymenaeus and Philetus, who have departed from the truth. They say that the resurrection has already taken place, and they destroy the faith of some. ~ 2 Timothy 2:14-18
But mark this: There will be terrible times in the last days. People will be lovers of themselves, lovers of money, boastful, proud, abusive, disobedient to their parents, ungrateful, unholy, without love, unforgiving, slanderous, without self-control, brutal, not lovers of the good, treacherous, rash, conceited, lovers of pleasure rather than lovers of God— having a form of godliness but denying its power. Have nothing to do with such people.
They are the kind who worm their way into homes and gain control over gullible women, who are loaded down with sins and are swayed by all kinds of evil desires, always learning but never able to come to a knowledge of the truth. Just as Jannes and Jambres opposed Moses, so also these teachers oppose the truth. They are men of depraved minds, who, as far as the faith is concerned, are rejected. But they will not get very far because, as in the case of those men, their folly will be clear to everyone. ~ 2 Timothy 3:1-9
For there are many rebellious people, full of meaningless talk and deception, especially those of the circumcision group. They must be silenced, because they are disrupting whole households by teaching things they ought not to teach—and that for the sake of dishonest gain. . . . They claim to know God, but by their actions they deny him. They are detestable, disobedient and unfit for doing anything good. ~ Titus 1:10-11, 16
Do not be carried away by all kinds of strange teachings. It is good for our hearts to be strengthened by grace, not by eating ceremonial foods, which is of no benefit to those who do so. ~ Hebrews 13:9
I say this because many deceivers, who do not acknowledge Jesus Christ as coming in the flesh, have gone out into the world. Any such person is the deceiver and the antichrist. Watch out that you do not lose what we have worked for, but that you may be rewarded fully. Anyone who runs ahead and does not continue in the teaching of Christ does not have God; whoever continues in the teaching has both the Father and the Son. If anyone comes to you and does not bring this teaching, do not take them into your house or welcome them. Anyone who welcomes them shares in their wicked work. ~ 2 John 1:7-11
I wrote to the church, but Diotrephes, who loves to be first, will not welcome us. So when I come, I will call attention to what he is doing, spreading malicious nonsense about us. Not satisfied with that, he even refuses to welcome other believers. He also stops those who want to do so and puts them out of the church. ~ 3 John 1:9
Dear friends, although I was very eager to write to you about the salvation we share, I felt compelled to write and urge you to contend for the faith that was once for all entrusted to God’s holy people. For certain individuals whose condemnation was written about long ago have secretly slipped in among you. They are ungodly people, who pervert the grace of our God into a license for immorality and deny Jesus Christ our only Sovereign and Lord. . . . These people are blemishes at your love feasts, eating with you without the slightest qualm—shepherds who feed only themselves. They are clouds without rain, blown along by the wind; autumn trees, without fruit and uprooted—twice dead. They are wild waves of the sea, foaming up their shame; wandering stars, for whom blackest darkness has been reserved forever. . . . These people are grumblers and faultfinders; they follow their own evil desires; they boast about themselves and flatter others for their own advantage. ~ Jude 1:3-4, 12-13, 16
Nevertheless, I have a few things against you: There are some among you who hold to the teaching of Balaam, who taught Balak to entice the Israelites to sin so that they ate food sacrificed to idols and committed sexual immorality. ~ Revelation 2:14 . . . Nevertheless, I have this against you: You tolerate that woman Jezebel, who calls herself a prophet. By her teaching she misleads my servants into sexual immorality and the eating of food sacrificed to idols. ~ Revelation 2:20
These are the false teachers and what they taught and did, whether out of Jewish exclusivity or pagan inclusivity … whether out of piety or selfishiness.
You learn a lot about these false teachers from those phrases I put in italics. They love to be first and call themselves prophets; they slip in secretly; they will lie, lie about where their teaching came from, flatter, cajole, take control of others, take over their homes, will not welcome others, and cause divisons and controversies. They are boastful, proud, arrogant, ungrateful, unholy, without love, unforgiving, slanderous, without self-control, brutal, treacherous, rash … the adjectives go on and on. (You’ve got to admire Jude’s very poetic description of them!) They like to quarrel about words. They are control freaks. They must have their own way. And some of them hope to make money from teaching what they think they know. If that were the worst of it, one could teach them and ignore them – keep away from them; not associate with them – if they ignored the teaching, so that they would be shamed.
But it’s what they teach that makes it impossible for them to repent; they confidently assert the rightness of it; their consciences have been seared. And what they teach include these heresies: impose circumcision and kosher dietary laws; cause trouble over celebrating holidays; encourage participation in idolatry; teach myths and genealogies as crucial; add worship of angels; forbid marriages; that Christ has already come; deny that He is Lord; and deny that He came in the flesh.
All of these things stab at the very heart of Christian faith: the sufficiency of the blood of Jesus manifesting the love and grace of the one and only God. They contradict the gospel of Jesus Christ.
These were no mere quibblings over what can or can’t be done in worship; who can or can’t preach Christ and Him crucified; or how many angels can dance on the head of a pin.
But hear me out on this, please.
When quibblings are elevated to a level that rivals the sufficiency of Christ to save, they become heresies. They don’t even have to produce the kind of personalities described above, although they can and probably will. Whatever empties the cross of its power and causes divisions (1 Corinthians 1:20) almost always is – or becomes – extricated with personalities and ego and personal preferences.
Those are the kinds of personalities Jesus had to deal with among the Pharisees and Sadducees, who had elevated their human teachings to the level of law and attributed them to God – even though some schools of human teaching didn’t agree with others (Matthew 2:22-23).
Quibbling matters are earthly things (Colossians 3:1-17); and when they become elevated to something more than they are, these teachings of men render worship vain (Matthew 15:9, Mark 7:7).
Ultimately, they bring swift destruction to the one who teaches them.