A position in an organization; not to be equated with the possession of priestly authority. Offices are created by people, and offices in the church are a matter of vote by the members, placing someone into a position (making offices of the church coincident with priesthood authority is another matter). Joseph Smith and Oliver Cowdery, for example, were elected to be the First and Second Elders of the church in 1830 — the Melchizedek Priesthood would not be restored until 1831. But they held the office of elder by virtue of the people accepting them by their vote. They could have elected them to be high priests or to any other office. Orson Hyde held the office of apostle (beginning in 1839) with, literally, no authority. Choose a title and have everyone vote; now one holds an office.1
1 “Cursed : Denied Priesthood,” Q&A, Jan. 7, 2018, 12–13, transcript of talk.