In simple terms QCD as a "background" usually refers to LHC research where hadronic jets create a lot of particles that clutter up the results you're trying to see. I think it has become a slang term and the use is discouraged.
ABCD method is a tool used to separate the particles of interest (signal) from the "other stuff" (background) made by the jets. It is a set of boundaries that relies on the fact that you have two independent distributions to distinguish between signal and background. See section 5.3 here http://dare.uva.nl/document/221955
This post imported from StackExchange Physics at 2014-04-13 14:34 (UCT), posted by SE-user user6972