In brief, the belief that is before the second coming of Jesus - those 'deserving' Christians who are truly following Christianity will be whisked away and will appear to disappear from earth.
It may be a primarily American belief - but I'm not sure. It seems a bit 'far out' to me - and the wiki entry for Rapture makes interesting reading (but I haven't really studied this subject).
It is interesting also to read the various predictions that have been made for when rapture will occur:
Some notable rapture predictions include the following:
1792 - Shakers calculated this date.[citation needed]
1844 - William Miller predicted Christ would return between March 21, 1843 and March 21, 1844, then revised his prediction, claiming to have miscalculated Scripture, to October 22, 1844. Miller's theology gave rise to the Advent movement.
1977 - William M. Branham predicted in 1962 that the Rapture could take place by 1977[citation needed]
1981 - Chuck Smith predicted that Jesus would likely return by 1981.[citation needed]
1988 - Publication of 88 Reasons why the Rapture is in 1988, by Edgar C. Whisenant.
1989 - Publication of The final shout: Rapture report 1989, by Edgar Whisenant. More predictions by this author appeared for 1992, 1995, and other years.
1992 - Korean group "Mission for the Coming Days" predicted October 28, 1992 as the date for the rapture.[37]
1993 - Seven years before the year 2000. The rapture would have to start to allow for seven years of the Tribulation before the Return in 2000. Multiple predictions.
1994 - Pastor John Hinkle of Christ Church in Los Angeles predicted June 9, 1994. Radio evangelist Harold Camping predicted September 27, 1994.[38]
1997 /2009 - In 1983 Richard Schiller (aka Elijah) claimed parallel alignment to all the WatchTower did with the 94 years of the rebuilt Jerusalem 537-443 BC as 1914-2008 AD. In this span of 49 Jubilees (Daniel's 7 weeks) as a 50th it fell on events for every event recorded everywhere in OT which ends with Artaxerxes 32nd year (Nehemiah & Malachi). He felt the events of year 20 equating 455 BC with 1996 AD were more probable an Armageddon than year 32 equating 443 BC with 2008 AD, placing Armageddon in 1997 and 2009 (the most ominous events of the year presumed split for Yom Kippur then Passover. Only Yom Kippur 2009 now remains to fulfill both events.)
2011 - Harold Camping's revised prediction has May 21, 2011 as the date of the rapture.[39]
2060 - Sir Isaac Newton proposed, based upon his calculations using figures from the book of Daniel, that the Apocalypse could happen no earlier than 2060.[40][41]
http://en.wikipedia.org/wiki/Rapture
(It looks like the predictions for 2009 and earlier were a bit off the mark!
To be honest, I was surprised that people believed this - but less surprised that many Americans did.
Perhaps eh can shed some light on this - he seems to hold a number of quaint beliefs and presents himself as a Biblical expert. I presume that he believes in rapture - because the Bible says so?
Cheers,
Shafique