The Rapture is a term referring to the belief, in certain fundamentalist Christian circles, that at some point in the final chapters of human history Jesus Christ will descend from heaven and simultaneously summon both dead and living Christians to meet Christ in the air. Upon this call, Christians will instantly, "in the twinkling of an eye," vanish from earth and rise up to heaven.
For an example of the scriptural basis of this belief see: 1 Thessalonians 4:16-17 NASB
16 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. 17 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.