洗完澡 means "finished the wash"
洗澡 means "wash or washing"
“洗” is a verb,and in chinese,we don't have the same grammer to describe the action is done or doing like english "wash---washed---washing",so we used to add some special words or character to explain the verb, and "完" has the same function of "ed" when put it after a verb.
such as :喝水(drink water) is the basic structure,
喝完水(drinked water) means I finished "drink water"
正在喝水 means I am drink-i-n-g water,here we add "正在" to describe the action is doing.
I hope the answer can help u to understand it.