The boil advisory is a precautionary measure put into place to make certain that water quality has not been compromised. While on a boil advisory, you should not consume any City water unless it has been boiled for 10 minutes.
There is no danger in showering while under a boil advisory (just be careful not to drink the water as you shower or bathe.)
If you are under a boil advisory and need to give water to your pets, it is a good idea to boil water for your pet as well.