The CPU is the brain of your machine which gathers information, via the control unit, from your installed memory modules, and processes instructions, via the logic unit, in order to run your programs. The CPU comes with varying clock speeds, which determine the number of instructions executable per second, and many other features which allow for faster and smoother execution.
A faster-clock CPU installed in your machine will allow you to perform these calculations and instructions faster, which in practical terms means being able to quickly access programs, read memory and execute the functions within those programs. For example, in a video conversion operation (converting one format to another), the processing times will be much less if you have a dual-core processor installed. When using a program like Photoshop or Paint Shop Pro, the effects you apply to an image use processing power also.