The core is the thing that runs the programs.
Think of a core as a worker in a plant. with a single core CPU (1 plant worker), that worker may be able to do a single task really quickly. But if you have a quad core CPU (4 workers), you could have 4 workers all doing the same thing (4 times the work) or doing 4 separate things. Either way, the more cores, the more simultaneous things can be run at once.
the GHz is the speed. the higher that number, the faster those core's work. anything above 3GHz is good.