A CPU, also called Microprocessor, is the brains of your PC.
The most common used CPUs are from either AMD or Intel.
(NEVER buy an Intel CPU...those guys are evil!)
The best way to compare CPU's (performance, powerconsumption, price) is to check benchmark lists.
Never buy the newest CPU, as the price usually is extremely high when just released but will come down after some time.
The following link shows a comparison of benchmarks (both Passmark, Sandra and 3DMark) that 5KW has done on random PCs during the years.
PC benchmarks - tests done by 5KW
Recently, it is very hard to find some updated benchmark charts.
Some charts for CPU and Graphic comparison, that I have been using lately (many benchmark charts can be found here):
link to notebookcheck CPU and GPU
link to PassMark CPU, GPU, HDD
link to Techarp