A base layer fits like a second skin, and helps quickly wick moisture away from your body. This helps keep you cool when it's warm out, and warm when it's cool out. Ultimately base layers regulate your body temperature and benefit you by keeping your focus where it should be - on your game.
A compression layer has the added advantage of helping to support your muscles, and keeping them warmed up during periods of lower activity. The grippy fit of compression layers have also been shown to aid performance in sports that require 'explosive' movements. We're thinking of your golf swing here, of course!