A base was any place or structure, such as a headquarters, that was used as the center of operations by a government, organization, or military, often otherwise described as a base of operation(s). The base where an individual or starship was posted was known as its home base. (TOS: "Arena", "Journey to Babel", "A Private Little War"; TAS: "The Time Trap")
In 2268 after the USS Enterprise entered Romulan space, a Romulan commander ordered the ship to follow the Romulan flagship to their home base where the crew would be processed and released to Federation Command. (TOS: "The Enterprise Incident")
When James T. Kirk, Spock, Abraham Lincoln, and Surak were pitted by the Excalbians in a match of "good" versus "evil" in 2269, Kirk took command of the group and found a location they could use as a base, as it was "defensible" and their enemies "can't approach without being seen." (TOS: "The Savage Curtain")