This is probably the most misunderstood aspect of handicapping in golf.
A 10-handicapper should shoot 10 over par. That’s the standard view among the uninitiated. In fact, a golfer’s handicap reflects his potential to score well, not his usual scores. The handicap index is a tweaked average based on only the 10 best of a player’s 20 most recent rounds. It is then adjusted for the course to be played according to that course’s difficulty ratings, to create a course handicap. On average golfers with official handicaps (only about 20% of all golfers) will tie or beat their course handicap only once in every five rounds.
Quoted from: online.wsj.com.