This seems to be big thing in RPG's but I suppose it can include other things too. The example that inspired this was from an RPG though.
See, I was reading on TVTropes' Character Sheet for Serge from Chrono Cross that "All he was ever trying to do was make a necklace for his girlfriend!" It struck me as both hilarious and interesting. You contrast where they began and where they ended and the two things are so far apart that you and whatever protagonist you're thinking of never could have seen it coming.
So the topic...well, here's an example to show you what I'm thinking:
Serge
The Beginning: He was trying to make a necklace for his childhood sweetheart.
The End: He defeats the supercompouter AI that rules the alternate dimension where he died, kills the dragon god from the future where reptiles ruled, and destroys the alien abomination merged with an ancient magic princess in order to keep it from annihilating all of space and time.
Basically, the type of protagonists relevant here are nice, simple little folks doing something perfectly routine until they get sucked into giant, crazy adventures without even meaning to. The bigger the contrast between the beginning and end, the more absurd the differences, the better.