Well, a "core" is the processor itself. The place where are the calculations are performed.
More cores = better multitasking, higher tdp
Now if you have 2 cores running at 3ghz this means that your cpu has 2 cores BOTH running at 3 ghz
If you have 4 cores at 3ghz it means you have 4 cores ALL running at 3 ghz
etc...
Performance: It depends on the architecture, atchitecture is how many instructions will be executed every hz(1 ghz = 1 billion hz/seccond)
When you reach a quad core (or dual core with hyperthreading) then games will not get a very big performance jump.
Your cpu is a dual core.
And an example of the architecture effect=
6 core cpu with slow architecture running at 4 ghz < dual core with hyperthreading with faster...