It's a way of saying "from a material". For example you could 'make a statue out of marble' or 'make a vase out of clay' So in the song she's saying she can transform him into a man.

Try not to think of "out of" as the two words "out" and "of" separately. Think of "out of" as one, unified word with a space between them. Think of "out of" as completely different from "out" and "of". I will contradict myself a little bit here, but let's use Lana's example from earlier. "A statue made out of marble" is talking about "a statue of marble" or "a marble statue". A gold ring is made out of gold. OR: A ring of gold is made out of gold. A clay vase is made out of clay. Now, referencing your question, what can you say about "I'll make a man out of you." A man is going to be made out of you. This means that "you" are not a man, but the speaker will make you a man. Usually a phrase like this would be used to a small boy, or a man who doesn't act "manly". Normally when it is used, it's derogatory or offensive. But, other times it may not be offensive. For example, your English teacher will make a great English speaker out of you! Your English teacher will make you a great English speaker. It's tough to explain, but I hope this helps. Good luck!