When you do something quickly, you do it really fast — like when you quickly eat breakfast so you won’t be late to school.
The adverb quickly can describe any action that’s done at great speed. If you see a wolf running quickly, that means it’s moving rapidly and you’d better hide quickly. Quickly can also carry the sense of doing something without delay or hesitation. Sometimes quickly has a connotation of not putting much thought or effort into something, like when you quickly do your math homework.