A favor was an action performed by one person to the advantage of another.
In 2368, Captain Jean-Luc Picard noted in his captain's log that "To cross the Neutral Zone, I will require a cloaked ship. To that end, I have set a course for the Klingon homeworld. After all we did for Gowron during the recent war, I am certain he will be happy to return a favor." (TNG: "Unification I")