WU; work unit; set of data that needs to be calculated, the client downloads one to your computer, processes it, returns the results back where its verified, if correct/expected result is returned, you'll receive full credit for completing a small piece of the larger puzzle. Failed, bad or miscalculated units receive partial or no credit. (Basically)
The different cores is the software used to crunch the data. Core15 (nVidia) and Core16 (AMD/ATI) are used for older gpu units, they're being phased out in favour of a more unified folding core, Core17; there's different cores for cpu units as well.