The theology behind the Left Behind books and films is what is called premillennial dispensationalism. It is held by fundamentalists and some but not all evangelicals.
The basic idea is that history is divided into different ages or dispensations. In each new age, God progressively reveals himself to humanity in new ways, and humanity is held responsible for that revelation–often failing in which God responds by inaugurating a new dispensation.
According to this scheme, humanity now lives in the Church Age or “the Age of Grace.” This period started on the Day of Pentecost and will continue until the rapture of the church. Some people identify this time period with the time between the the 69th and 70th week of Daniel 9:24.
After the rapture of born again believers, again according to this scheme, there will be 7 years of Tribulation on earth, 7 years of divine judgment.
Following these 7 years will be the next dispensation–the millennium. This will last for 1,000 years, and during this time Christ himself will rule on earth. The Jewish nation would be reestablished, with Christ as king. The saints who had died or were raptured and the righteous survivors of the Tribulation will dwell in this kingdom.
At the end of this dispensation, the final judgment of Revelation 20 will take place. The world will be destroyed by fire, and a new heaven and new earth created in which the righteous will live with God for eternity.