The difference is that if you don't compress the signal before it goes into your recording medium (Keyboard or computer), you risk the signal possibly clipping the Analog-to-digital converters. Back in the day of analog only gear (Tape decks, reel-to-reels, etc) you could overdrive the signal and it would result in a mild saturation (distortion), that was very warm and pleasing. It is the most sought after characteristic of Analog gear. Digital gear uses converters to change the signal from analog to digital. problem is that you can't overdrive the converters like you can with tapes. The signal won't get warm and fuzzy, what you get is an absolutely harsh nasty sound (kinda like a cat caught in a blender). The human voice is one of the most dynamic instruments around. Why risk having to trash a perfectly awesome vocal take, because you stepped a little too close to the microphone. A compressor has the ability to tame those peaks in the signal that could otherwise destroy a perfectly good vocal take. It can also take very low volume parts and boost them up a bit, giving you a more uniform signal with better signal-to-noise ratio. Most good compressors also feature a gate section to remove unwanted hiss when no sounds are passing through (usually adjustable), a limiter section, which does just that, no sound is allowed to pass through above the volume you set (I usually set the compressor to run a few decibel underneath the limiter, and the limiter set just below the threshold for the converters). They'll also include sidechains for compressing certain frequencies only or triggering the gate (i.e. kick drum signal running into sidechain opens gate allowing signal running through compressor to play while gate is open, often a bass guitar...real popular dance music trick). At the very least if you get nothing else get a compressor.
