Becky P actually gave a fairly complete answer. I'll try to make it simpler.
First, Sirius had been convicted of killing a whole bunch of Muggles, one of my dad's best friends (Peter Pettigrew), *and* was blamed for leading Voldemort to my parents' hideout. So, everyone thought Sirius was an insane, murderous Death Eater loyal to Voldemort and responsible for my parents' death. They figured I was the next logical target for a serial murderer loyal to Voldemort (who "died" while trying to kill me).
BUT
In fact, Sirius was never out to get me, never killed those Muggles and never killed Peter Pettigrew. Also, Sirius was *not* the Secret Keeper for my parents, it was Pettigrew. So, in fact, Pettigrew was responsible for *everything* that had been blamed on Sirius (except for his own death, obviously, though Pettigrew framed Sirius for that by turning into a rat at the last second).
SO, you can see why people *thought* that Sirius had a very strong motive to kill me, and also that he *never did* have a motive to kill me. He was after Pettigrew - the Muggle-killer, the one who had framed Sirius for the murders (causing him to be sent to Azkaban), the one who had actually betrayed my parents (Sirius' friends) to Voldemort. Sirius found out that Pettigrew was still alive, and Sirius (*only* Sirius) knew that Pettigrew was responsible for all of these crimes.
Harry