Moriarty was more or less responsible (in various ways) for all the crimes committed in the first season, which were all foiled by Sherlock. Plus he's obsessed in general. If you want detailed info you can check the wikia page (lots of spoilers though) - http://bakerstreet.wikia.com/wiki/Jim_Moriarty
6 months ago
Last edited at 3:24AM on 10/5/2013
He said, or rather meant, "I owe you a fall". He means that he needed to take Sherlock down, to be his downfall. Also, Sherlock did cause him trouble in that he was solving his crimes, foiling his dastardly plans (that makes him sound like a pirate). He needed Sherlock to die so that he could keep working. He was letting Sherlock know this in advance, I guess. Does that make sense?