The biggest reason is to shorten the lag period. During that lag period, while the yeast are reproducing, they're also generating byproducts that can introduce off flavors into your beer. Typically those get cleaned up if you give them enough time, but not always. Anyway, with a starter, you build up a large population of yeast before they ever hit the beer, so they spend less time reproducing, thus less lag, thus less byproducts to clean up.
Some side benefits, like mrrshotshot pointed out, are that the shorter lag time gives other nasties less time to take over within your wort, and also let you know that your yeast is indeed healthy before you pitch it into your fermenter.