The rapture, or the secret rapture, is the belief that Christ will initiate His second coming in two stages, and the first stage will be the transporting of believers to Heaven at the beginning of the Tribulation.
The word rapture does not appear in the Bible, but it is a term frequently used in conjunction with events relating to the Second Coming of Jesus. The meaning or definition of rapture is the idea that the coming of Jesus will take place in two separate stages. The first will be a secret rapture—or carrying away of the saved to heaven—at the beginning of a seven-year period of tribulation, during which the antichrist will appear. The second phase occurs at the close of this time of tribulation when Jesus will return to Earth in triumph and glory.
~ Bibleinfo.com, "What is the rapture?"
The largest problem with this belief is that there is very little biblical evidence for it, and that such as it exists requires a torturous interpretation of Scripture.
The second largest problem with this belief is that it means Christ's second coming is not actually His second coming at all because it requires that He returns twice more instead of once more. Therefore, in reality, what is commonly called His "second coming" would actually have to be His third coming.