Depends on the context.
Emotionally, it means being elated.
Theologically, it means Jesus taking believers both dead and living from the earth into the sky to be with Him at His second coming. See the books of First Corinthians chapter 15 verses 50-58 (I Cor.15:50-58) and First Thessalonians chapter 4 verses 13-18 (I Thess. 4:13-18) in the New Testament section of the Bible. The word rapture comes from the Latin word raptus 'to seize'-hence Christians being taken up (or seized) alive by the Lord into heaven.
Same reason birds of prey are called raptors from the way they snatch their prey with their talons- the sharp claws on their feet.