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.
The Navy conducts exercises at sea from time to time, operations that civilians refer to as "war games." The goal is to train the ships' crews to deal with the operational tempo, lack of sleep and some of the stresses of being in fluid and uncertain situations at sea.
I was one of the OODs of one of the ships in the exercise. My ship had a modest AAW defensive capability. That was simulated by the firing of a green flare from a Very pistol. For the duration of the exercise, the OODs wore a holster with the Very pistol and several flares.
There was a recognition procedure to identify friendly and hostile aircraft. If I remember correctly, friendlies were to approach ships by flying a certain true course. No radio calls were to be made.
When the EWs detected a contact, the information was passed up to the Bridge over the JA phone circuit. The lookouts were also on the JA circuit, so they would look for something. Because of this, the bearings to any possible threats were sent up as relative bearings (0 degrees being "dead ahead").
So there I was, on watch. The call came up: "Hostile aircraft, bearing 080." The lookouts almost immediately reported "air contact, 3 o'clock". I looked, sure enough, a helicopter was flying directly at the ship.
I loaded the Very pistol, raised it, and fired the flare.
The problem, of course, was that when one added the ship's course to the relative bearing of the air contact, the helicopter was on the "safe course".
The pilots, understandably, were not amused. They broke radio silence and rained some abuse down upon the R/T operator in CIC.
The Captain, though, was more sanguine about it. He came up to the Bridge and asked me what happened. I told him and apologized for fucking up. He shrugged and asked me if I had ever heard the Simon & Garfunkel song "the Boxer". I said I had and I guess my puzzlement showed.
He told me that there is a line in the song that "a man hears what he wants to hear and disregards the rest". He told me that I expected to see an enemy aircraft and that I saw what I thought I would see and that, in a hot war, people were always going to get killed that way. He told me the real trick was to be able to make fast decisions and yet be alert enough to question myself to make reasonably certain that I really knew what was going on.
I kept the shell casing from the Very flare for many years, eventually losing it in a move somewhere along the way.