The CPU, which stands for Central Processing Unit, is the brain of the PC. It is often referred to as the "processor" or "chip". The CPU directs, coordinates and communicates with the hardware components and performs all of the "thinking". What a CPU actually does is perform mathematical calculations. It is the software that people write that translates those calculations into useful functions for us.
The speed of the CPU, now measured in gigahertz (GHz), generally speaking relates to the number of calculations it can perform in one second. Higher gigahertz ratings translate to a greater number of calculations or instructions per second. It is more complicated than that, but it is a reasonable way to think of the speed.
As the speed of new CPUs increase, the difference is becoming less obvious to computer users. A CPU that is twice as fast as another one will not result in a PC running twice as fast. The CPU has to wait for other, slower components and for the user too. The CPU spends a lot of time sitting idle, waiting for something to do.
CPUs have something called a "cache" or memory cache. The memory cache is where information is stored that the CPU is likely to need soon. This memory is in addition to the normal memory installed in a PC. The difference is that the cache is built right onto the CPU (and/or very near the CPU), and it is much faster than conventional memory. Cache memory was developed to reduce the time the CPU had to wait while information was retrieved from the standard memory.