Dynamics. The thing that makes most music come to life. Have you ever heard a performance where the music goes from piano to fortississimo or quiet to very loud? It is quite captivating isn't it? Well in the digital world of recording this sometimes becomes a problem.
Since the microphone works like your ear and you have an instrument right in front of it, sometimes the sound source is too big for the microphone to output it correctly. This is where compression comes in. A compressor's function is to lower these high peaks to an appropriate level. This way you can keep the dynamic feel without getting distortion through your speakers.
Just like a compressor, there are other signal processors that improve a recording by getting rid of extra noise that manages to get in such as an expander or gate. An expander does the opposite of a compressor it increases output level as input level increases and decreases output as input decreases. A gate is exactly what it sounds like. A gate is the mid-point where sound either goes through or stays out. We can go into much more detail with signal processors but the main idea from this is that you can manipulate your signal however you want to get the best out of it.