"the world is beating you down" means that everyone and everything is (or seems to be) trying to crush you or knock you back. "I'm around through every mood" probably means "I'm with you through every one of your different moods (good or bad)".
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osama91 "the world is beating you down, I'm around through every mood".The singer says that his love is beautiful even when she's crying because she's had a bad time, or bad luck. The singer says then that he will stay by her and love her even when she's sad, happy, angry, depressed, etc.