One who gives moral but not material support. The allusion is to boxing or prize-fighting, where each combatant has a bottle-holder to wipe off blood, refresh with water, and do other services to encourage his man to perserve and win.
“Lord Palmerston considered himself the bottle-holder of oppressed States. ... He was the stead-fast partisan of constitutional liberty in every part of the world.” —The Times.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894