Think of it as data compression that shows you the notes you're most likely to play, without taking up space for notes you probably won't.

If there's a piece in C, for example, in most traditional Western music you're unlikely to play off-key notes. So why take up valuable space for those when you can denote that unlikely event with a sharp/flat symbol?

Traditional music notation made no sense at all to me until I realized this.

Edit: For those that don't know, in most western music you're only going to use 8 out of the 12 possible notes most of the time. This is not universally true especially of modern non-pop music, but traditionally if you played off-key notes people thought you might summon evil spirits so it's easy to understand why things would be written down this way. Not only is it space efficient, but you wouldn't accidentally summon the devil. To summon the devil you have to really want to and write a flat or sharp in there.