"To clean" means simply to make something clean.
"To clean up" implies that you are cleaning and/or tidying something which somebody else has made dirty or messy, deliberately or accidentally.
"I cleaned the dusty window." (Nobody put the dust there. It simply settled there over time.)
"I will clean the car." (Nobody made the car dirty deliberately.)
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"I cleaned up after the party." (The guests had left empty bottles, cakes and spilt wine.)
"I will clean up the vomit." (Somebody has been sick on the floor.)
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There is also a colloquial meaning, which refers to winning money:-
"He cleaned up at Poker." (He won the card game.)