To reproduce is to make more, either by having babies or creating copies. Parents and copy machines both reproduce.
To produce is "to make something," and re means “again,” so reproduce literally means to “produce again.” When animals and plants make more of their own kind, they reproduce. Plants reproduce asexually, and people reproduce through childbirth. You can also reproduce a book by printing more copies or a computer file by copying it. Reproducing always creates more of something.