Willpower, also known as mental strength, and strength- or force of will, was an individual's ability to make and carry out decisions.
In 1957, Jack expressed his wonder to T'Mir that fakirs could almost stop their hearts using willpower. (ENT: "Carbon Creek")
In 2266, the "good" side of Captain James T. Kirk noted in his log that he seemed to have lost his strength/force of will after being duplicated. Spock also observed the decline in a later entry. (TOS: "The Enemy Within")
Willpower could go a long way towards surviving severe injury or illness. Doctor Leonard McCoy described Joe Tormolen as a man who normally didn't give up, yet he lost the will to live anyway. (TOS: "The Naked Time")
In 2365, Ira Graves described himself as having an iron will. (TNG: "The Schizoid Man")
The aunt of Lathal Bine was known as "the iron-willed woman of Beta moon". (TNG: "The Host")
In 2375, Seven of Nine stated that she had assumed that romantic love was a Human weakness, but saw that it could also be a source of strength. (VOY: "The Disease")