The term hollywood shower is common slang from the US Navy. When you are on a ship, floating on a saltwater sea in very hot climates, you tend to want to take a nice shower after a 12-hour shift. Unfortunately, the ship can only produce a finite amount of water, and it usually does not operate efficiently in hot, dry areas of the world (like the Persian Gulf).

After taking your sweaty, grimy and greasy self down to the enlisted berthing compartments, you can take a shower - for less than two minutes. All of the ships I was assigned to (all of them small "tin cans") had a button you pushed to turn on the water. You had to get wet enough to get soapy, because after about a minute it would turn off. After you soaped and scrubbed yourself (including your hair), you would hit the button again to rinse.

A hollywood shower is when you have an abundance of water, and you get to hit the button five or six times. It is a small luxury that you take advantage of whenever you can. When a ship tied up to a pier, they would take on fresh water, and hollywood showers were the norm. If you were out at sea, and the water levels were low, you did not take hollywoods. If you did, your fellow shipmates would admonish you, and you could get assigned some menial tasks such as scrubbing down the back of the toilets.

Note that this was for the enlisted folks. The officers could take hollywoods whenever they liked.