To hold on to something, usually tightly.
Jack almost fell off the cliff, but managed to hang on until help came.
To hold a lead in a race or other contest while one's opponents try to rally.
Bunning, staked to a 6-0 lead in the first inning, hung on to heat the Dodgers 6-4.
The favorite horse opened an early lead and hung on to win as two other horses almost passed him in the final stretch.