The process of elimination was a method for determining an answer by removing possibilities until only one remained.
It was evidenced in the saying coined by one of Spock's ancestors, "if you eliminate the impossible, whatever remains, however improbable, must be the truth." (Star Trek VI: The Undiscovered Country)
In 2267, when attempting to locate the source of a "radiated energy pulsation" coming from the planet Pollux V, Spock suggested that Hikaru Sulu use the process of elimination to determine where the power source was not. Sulu initially questioned whether the first officer really meant him to search the entire planet, but ultimately performed the task as instructed. (TOS: "Who Mourns for Adonais?")