E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
means simply to lower, and the idea usually associated with the word is derived from a custom in gladiatorial sports: When a gladiator acknowledged himself vanquished he lowered (submitted) his arms as a sign that he gave in; it then rested with the spectators to let him go or put him to death. If they wished him to live they held their thumbs down, if to be put to death they held their thumbs upwards.