1 Thessalonians 4:15-18
For this we say to you by the word of the Lord, that we who are alive and remain until the coming of the Lord, will not precede those who have fallen asleep.
For the Lord Himself will descend from heaven with a shout, with the voice of the archangel and with the trumpet of God, and the dead in Christ will rise first.
Then we who are alive and remain will be caught up together with them in the clouds to meet the Lord in the air, and so we shall always be with the Lord.
Therefore comfort one another with these words.
I recommend http://www.gotquestions.org/rapture.html for concise Q&A on the subject. For example: Question: "What is the Rapture of the church?"
Answer: The word “rapture” does not occur in the Bible. The concept of the rapture, though, is clearly taught in Scripture. The rapture of the church is the event in which God removes all believers from the earth in order to make way for His righteous judgment to be poured out on the earth during the tribulation period. The rapture is described primarily in 1 Thessalonians 4:13-18 and 1 Corinthians 15:50-54. God will resurrect all believers who have died, give them glorified bodies, and take them from the earth, along with those believers who are still alive and who will at that time also be given glorified bodies. “For the Lord Himself will come down from heaven, with a loud command, with the voice of the archangel and with the trumpet call of God, and the dead in Christ will rise first. After that, we who are still alive and are left will be caught up together with them in the clouds to meet the Lord in the air. And so we will be with the Lord forever” (1 Thessalonians 4:16-17).
The rapture will be instantaneous in nature, and we will receive glorified bodies at that time. “Listen, I tell you a mystery: We will not all sleep, but we will all be changed—in a flash, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, the dead will be raised imperishable, and we will be changed” (1 Corinthians 15:51-52). The rapture is the glorious event we should all be longing for. We will finally be free from sin. We will be in God's presence forever. There is far too much debate over the meaning and scope of the rapture. This is not God’s intent. Rather, in regard to the rapture, God wants us to “encourage each other with these words” (1 Thessalonians 4:18).
Recommended Resource: The Rapture: Who Will Face the Tribulation by Tim LaHaye.