Handicaps are meant to represent a golfer's potential rather than simply be an average of a golfer's scores. For example, someone who averages 20-over-par likely won't have a handicap of 20; his handicap will likely be several strokes lower than 20 because of the way handicaps are calculated.
An official handicap - one that is established through the auspices of a USGA affiliated club - is called a "handicap index." To establish a handicap index, a golfer needs a minimum of his five most recent scores, plus the course rating and slope rating of the courses played.
Once a handicap index is established, it is then used to determine a course handicap. A course handicap tells a golfer how many strokes he is allowed to take on a specific golf course; that is, a course handicap of 14 means the golfer will be able to deduct 14 strokes from his score throughout the round.
Handicap indexes are used so that golfers of widely different playing abilities can compete fairly against one another.
For a more in-depth explanation of handicaps see:
Overview of USGA handicapping system
How are handicap indexes calculated?
How do I use my handicap index on the golf course?
And for still more, see our Handicaps FAQ.