What is a double bogey?
Every hole has a par: the number of strokes a skilled player is expected to need. If you need two strokes more, you record a double bogey. On a par 3 that is 5 strokes, on a par 4 it is 6 strokes and on a par 5 it is 7 strokes. One stroke fewer is a bogey, one stroke more is a triple bogey.
Double bogey in Stableford
In a Stableford competition a net double bogey earns 0 points. From that point there is no reason to finish the hole, so you may pick up your ball.
Net double bogey and your handicap
Under the World Handicap System a net double bogey is the maximum score per hole that counts towards your handicap. That way a bad hole can never hurt your handicap calculation more than that.