The basic story is that Smith and Jones work for the government, managing the aliens who live here, even going so far as jailing some baddies amongst their number. One of the bad aliens (Boris the Animal) escapes, and goes back in time to kill Jones in the hope that he'll stop creating the Earth's defence system and allow his race to attack. Initially he succeeds. Only Smith remembers that Jones ever existed in the present, and vows to go back and save Jones (and help create Earth's defence system).
It sounds silly, but it's fun to watch all the same.