A choice was an act made by an individual when they decided between two or more possibilities or alternatives, or had the opportunity to make such a decision.
In 2254, as he experienced tiredness from commanding the USS Enterprise, Captain Christopher Pike contemplated resigning from his life as a Starfleet officer and choosing another life. Doctor Phil Boyce disagreed, saying that there was no other life for Pike. Boyce then said, "A man either lives life as it happens to him, meets it head-on, and licks it, or he turns his back on it and starts to wither away." In other words, the choice between living and dying.
Vina described Pike as a "perfect choice".
The Talosian Magistrate offered nourishment to Pike. When Pike suggested he might prefer starvation, he was given the unpleasant alternative of punishment by experiencing Hell-Fire. This convinced Pike into consuming the nourishment.
After Pike resisted Vina, the Talosians gave him a selection. He could choose between J.M. Colt and Una. Vina was not impressed with either, being skeptical that a union with Colt would produce intelligent offspring and, with Una, that "they'd have more luck crossing him with a computer." (TOS: "The Cage")
In 2368, in a conversation with Professor Berlinghoff Rasmussen, Captain Jean-Luc Picard said, "A person's life, their future, hinges on each of a thousand choices. Living is making choices." (TNG: "A Matter of Time")
In 2369, when the Klingons Lursa and B'Etor first visited Deep Space 9, they initially refused to surrender their weapons, against station policy. Chief of security Odo told them that it was their choice to either leave their weapons or leave the station. B'Etor asked him who he was and he replied that he was the one giving them the choice, at which point they surrendered their weapons. (DS9: "Past Prologue")