Gladiators' fights could be of three main kinds:

• ad igitum, in which the death of the rival wasn't necessary (one could surrender by raising the index finger);
• munerari, in which the loser could be saved (missio) or killed (jugula) as requested by the audience;
• finally, sine missione, in which the defeat of a gladiator necessarily lead to his death.

In the munerari fights the loser knelt with one arm behind his back as a sign of submission. He then asked for mercy or death. To ask for mercy he showed the sign Pollex Pressus. If he was heroically asking for his death he made the sign Pollex Versus. The audience responded by making the appropriate sign and shouting "LIFE" or "DEATH".
If he was granted mercy the gladiator would rise and the rival would be awarded a palm leaf. In the case of death... see above.

Apparently it is not known for sure how the signs Pollex Pressus and Pollex Versus were made, though it is popular nowadays to think that thumbs up signified 'life' and thumbs down 'death'.