Doing anything quietly means doing it while making very little noise. When you sneak down to the kitchen for that last piece of pie, you should tiptoe quietly past the rooms of your sleeping siblings.
If the librarian frowns at you, puts a finger to his lips, and says "Shhhh!", it means he would like you to speak more quietly while you're in the library. Use this adverb for anything you do in a soft, hushed, or faint way. Whisper quietly when you don't want to be overheard, and chew your food quietly unless you really want to irritate your brother.