In this case, it is not shorthand for "administration". An "admin" is a hotel room that is booked by all of the officers of a ship. It can serve as a crash pad or as a place to have a few drinks in private or as a place to change clothes or, if one is lucky, as a place to have a little quiet sex.
All of the officers chip in to pay for the cost of renting the admin for the duration of a port visit. The ones who make the most use of it are the no-loads in the Supply, Administrative and Operations departments. The officers in the Weapons department are usually neutral about it, as some may have the free time to use the admin and some may not. Generally, the engineers are against the whole idea, as they work longer hours both in port and at sea. Junior officers who are behind on completing their SWO qualification may also be against it.
Usually those who are against it get out-voted during the wardroom meeting. After several of those, the engineers can (and do) develop hard feelings about it.