Anything can be washed and this verb perfectly corresponds to Russian verb "мыть". However you can "умывать" (also wash) only your or somebody's face (one exception I'll tell you later). Ending "ся" initially meant to mean "себя" (self) in Russian. So, умываться=умывать себя and as I said, because you use this word only for washing face it means exactly washing your face. If you are washing your body - you are "моешься" ("моешь себя").
I hope this will help.
The exception I promised to tell you is an expression: "умывать руки". Example: "Я умываю руки. Делайте что хотите." Тhat means "I don't care any more and I withdraw myself from this business. You can do whatever you want to do".