The term come out refers to the act of exposing one's sexual or gender identity to family, friends, colleagues, etc., from whom it had been hidden before. The term is shorthand for "coming out of the closet." The closet is the metaphor for the hiding one does prior to coming out.
More About Come Out
Over the last decade the term has become more ingrained in the vernacular. Today people can be heard referencing how they have "come out" when they admit something dorky about themselves. However, it represents something very important. For many people, coming out is a frightening process involving a great personal and possibly even physical risk.