Jimmy Bane was a criminal from whom Anthony Cooper stole $700,000 in a retirement con. He attended the graveyard where the funeral of Anthony was taking place, probably to either catch Cooper, find a lead to finding him or to make sure he was actually dead.
He later showed up at Locke's house with an associate to question Locke about his father and the money. He made Locke empty his bag expecting to find his money. Instead he saw his work papers. He thanked Helen for making him coffee while they waited and left. ("Lockdown")