Hand for hand (abbreviated H4H) is a format used for certain stages of large multi-table tournament. While the format is in effect all tables must play the same number of hands - this means that as each table finishes its hand the players must wait until all tables have finished the hand before they can be dealt the next hand.
The format is mainly used at two stages - firstly H4H is used at the bubble when the final eliminations prior to the in the money finishes are determined. Secondly, H4H is sometimes used just prior to the final table when payouts often escalate considerably for each finishing position.
The purpose of H4H is to prevent players (especially short stacks) from stalling for time at these crucial stages in hopes that enough eliminations will occur at faster tables to allow them to cash. Play at this stage tends to be extremely tight, especially if a player is not in imminent danger of being blinded or anted out of the tournament.