The antichrist appears in the NT only in the epistles of John. Despite Hollywood and the popular imagination, the antichrist does not appear in Revelation. (And BTW 666 is the number of the Beast who is not Satan.)
In the epistles of John, the antichrist is anyone who does not profess the proper doctrine about Christ, that Christ is the Son of God (in the supernatural sense) and came in the flesh. Denying that Jesus was the Son of God, that Jesus has been an ordinary human, removed the power of the sacrifice. Denying that Jesus came in the flesh also removes the meaning of the resurrection. Both of these were key tenets of proto-Christianity.
There are many antichrists, deniers of the divine nature of Jesus. John is talking in particular about members of his own community who left. He is cautioning remaining members not to fall into error and lose eternal life.
1 John 2
18 Children, it is the last hour, and as you have heard that antichrist is coming, so now many antichrists have come. Therefore we know that it is the last hour. 19 They went out from us, but they were not of us; for if they had been of us, they would have continued with us. But they went out, that it might become plain that they all are not of us. 20 But you have been anointed by the Holy One, and you all have knowledge. 21 I write to you, not because you do not know the truth, but because you know it, and because no lie is of the truth. 22 Who is the liar but he who denies that Jesus is the Christ? This is the antichrist, he who denies the Father and the Son. 23 No one who denies the Son has the Father. Whoever confesses the Son has the Father also. 24 Let what you heard from the beginning abide in you. If what you heard from the beginning abides in you, then you too will abide in the Son and in the Father. 25 And this is the promise that he made to us—eternal life.
1 John 4
1 Beloved, do not believe every spirit, but test the spirits to see whether they are from God, for many false prophets have gone out into the world. 2 By this you know the Spirit of God: every spirit that confesses that Jesus Christ has come in the flesh is from God, 3 and every spirit that does not confess Jesus is not from God. This is the spirit of the antichrist, which you heard was coming and now is in the world already.
2 John 1
7 For many deceivers have gone out into the world, those who do not confess the coming of Jesus Christ in the flesh. Such a one is the deceiver and the antichrist. 8 Watch yourselves, so that you may not lose what we have worked for, but may win a full reward. 9 Everyone who goes on ahead and does not abide in the teaching of Christ, does not have God. Whoever abides in the teaching has both the Father and the Son. 10 If anyone comes to you and does not bring this teaching, do not receive him into your house or give him any greeting, 11 for whoever greets him takes part in his wicked works.