A Quad core has four cores. They can all operate one thread per core, totaling to four. A Dual core has two cores that can do two things at once.
Hyper threading is a technology that was used for single cores, that they could handle two threads at once, but it had the feeling as it if had two cores, but yet it's one core. Think Hyper-threading as a women...they can do two things at once, while men can do one.
New Quad cores now hasthe feeling of 8, but the HT technology can have each core do two things at once, totalling to 8.