What is the rapture all about?

It is when Christ calls his church to him, to meet him in the air

1Thes 4:13-18
13    But I would not have you to be ignorant, brethren, concerning them which are asleep, that ye sorrow not, even as others which have no hope.
14    For if we believe that Jesus died and rose again, even so them also which sleep in Jesus will God bring with him.
15    For this we say unto you by the word of the Lord, that we which are alive and remain unto the coming of the Lord shall not prevent {precede} them which are asleep.
16    For the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with the trump of God: and the dead in Christ shall rise first:
17    Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord.
18    Wherefore comfort one another with these words.

1 Cor 15:45-54
45    And so it is written, The first man Adam was made a living soul; the last Adam was made a quickening spirit.
46    Howbeit that was not first which is spiritual, but that which is natural; and afterward that which is spiritual.
47    The first man is of the earth, earthy: the second man is the Lord from heaven.
48    As is the earthy, such are they also that are earthy: and as is the heavenly, such are they also that are heavenly.
49    And as we have borne the image of the earthy, we shall also bear the image of the heavenly.
50    Now this I say, brethren, that flesh and blood cannot inherit the kingdom of God; neither doth corruption inherit incorruption.
51    Behold, I shew you a mystery; We shall not all sleep, but we shall all be changed,
52    In a moment, in the twinkling of an eye, at the last trump: for the trumpet shall sound, and the dead shall be raised incorruptible, and we shall be changed.
53    For this corruptible must put on incorruption, and this mortal must put on immortality.
54    So when this corruptible shall have put on incorruption, and this mortal shall have put on immortality, then shall be brought to pass the saying that is written, Death is swallowed up in victory.

First those Christians who were dead will be raised up and be made incorruptible, while at the same time we living Christians will be made immortal.   Then together we will all be caught up to meet Christ in the air, and stand before the judgement seat of Christ for our rewards if any are to be given.  This is also referred to as our gathering together unto him.  See "Some difficult to understand scriptures" link for a better breakdown of this passage below.

II Th 2:1-13
1    Now we beseech you, brethren, by the coming of our Lord Jesus Christ, and by our gathering together unto him,
2    That ye be not soon shaken in mind, or be troubled, neither by spirit, nor by word, nor by letter as from us, as that the day of Christ is at hand.
3    Let no man deceive you by any means: for that day shall not come, except there come a falling away first, and that man of sin be revealed, the son of perdition;
4    Who opposeth and exalteth himself above all that is called God, or that is worshipped; so that he as God sitteth in the temple of God, shewing himself that he is God.
5    Remember ye not, that, when I was yet with you, I told you these things?
6    And now ye know what withholdeth that he might be revealed in his time.
7    For the mystery of iniquity doth already work: only he who now letteth will let, until he be taken out of the way.
8    And then shall that Wicked be revealed, whom the Lord shall consume with the spirit of his mouth, and shall destroy with the brightness of his coming:
9    Even him, whose coming is after the working of Satan with all power and signs and lying wonders,
10    And with all deceivableness of unrighteousness in them that perish; because they received not the love of the truth, that they might be saved.
11    And for this cause God shall send them strong delusion, that they should believe a lie:
12    That they all might be damned who believed not the truth, but had pleasure in unrighteousness.
13    But we are bound to give thanks alway to God for you, brethren beloved of the Lord, because God hath from the beginning chosen you to salvation through sanctification of the Spirit and belief of the truth:

These above passages are not referring to the two great resurrections of the just and unjust, nor the great white throne judgement.  These occur during the wrath of God, but after the rapture.  These last judgements also involve all old testament believers and unbelievers up until the day of Pentecost.

Acts 2:1-4
1    And when the day of Pentecost was fully come, they were all with one accord in one place.
2    And suddenly there came a sound from heaven as of a rushing mighty wind, and it filled all the house where they were sitting.
3    And there appeared unto them cloven tongues like as of fire, and it sat upon each of them.
4    And they were all filled with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance.

This moment above marked the beginning of the true Christian movement, when believers could now be born again of Gods spirit.  From this moment until the time calls his church to be with him, will Christianity prevail as Gods true church on earth.   The rapture will signal the ending of the present Christian church and age.