I can give this a run, considering I was raised by them.
Essentially the Rapture is the start of the end of the war. All the true believers (and young of heart, aka those that are pure and have not been able to choose "salvation") are taken directly into heaven. Usually this happens by them leaving all their clothes etc, they just vanish and get free room and board in eternal paradise.
Now the rest of us get 7 years of horrible things which will most likely kill off 3/4ths of us. It's gonna suck. I'm talking Earthquakes, famine, plague, volcanoes from eqs, and bad jokes about cats. Also this Anti-Christ guy will show up and take over the world politically and spiritually or something, not important you'll probably end up dead from the riots.
So after all that happens, then Monsieur Jesus comes back to Earth and gives everybody a second chance that converted while all this horrible **** that he/"God" was causing. And also some of the people that converted and died get to come back before going into heaven... Or something.. There's a book series I'm mostly basing this off of, but that's beside the point.