It's basically two blocks wide, from Broadway to Bowery, and spans from Houston in the south to Astor Place in the north (although the area immediately surrounding Astor Place is usually just known as Astor Place.) Much like Soho it's a lot of old loft buildings with some new high-end buildings mixed end. It's very expensive real estate. I'm not sure you can say it's really "known" for anything in particular.
I always associate TriBeCa with families who want to live in lofts instead of the UES. It's a pretty bland expanse of converted industrial buildings - sort of a SoHo west but without the concentration of shopping. As bucket says, the Film Festival maybe.
