The CPU (or processor) is the central component of a computer. Everything task that happens on your computer, from running a document to browsing the internet to playing a game, is controlled by the CPU.
CPU power is primarily dependent on clock speed (measured in GHz) and the number of cores. Generally speaking, the faster the clock speed and the more cores a CPU has, the faster it will perform, although it isn't necesasrily the most cost-effective approach to choosing a CPU!
If you're looking to build a PC mainly for home or office tasks, like browsing, e-mail and documents, then you don't really need more than a dual core CPU. If you're planning on gaming, then going for quad core or higher would be ideal, and even more so for video editing or 3D modeling.