When you scrub something, you wash it forcefully. You might scrub your dirty bathtub with a brush and some bleach, for example.
When you scrub your floor, you use elbow grease — in other words, you work hard to get the floor clean. You might need to scrub your fingernails after a morning working on your car's engine, rubbing with a nail brush to get the grease off. Word experts think that scrub comes from the Middle Low German word schrubben, which also means "to scrub."