When a horse runs outside of the handicap it means that it cannot run off the correct weight for its official rating in the class it runs in.
For example, in a race, say the top weight is Rocky Two who has a handicap mark of 68.
The conditions of the race state that the top weight runs off 9st 7lbs and that the minimum weight a horse can run off is 8st 2lbs.
Another runner, Spats Columbo, runs off a mark of 47.
Theoretically he should run off a weight 21lbs lighter than Rocky Two (68 – 47 = 21), but that would mean he would be carrying 8st 0lbs.
So the fact he has to carry 8st 2lbs means that he is 2lbs wrong, or 2lbs outside the handicap.