Is this something you heard? The actual expression is 'I'm the brains and you're the BRAWN'. Brawn is physical strength. If you read it, and it actually said 'bronze', I have no idea.

Perhaps you meant to say "brawn", which means "physical strength in contrast to intelligence". Brain and brawn are often used together for contrast. Note that both words begin with the "bra" sound, which makes it an alliterative pair, a feature conducive to pairing.

It should be "brawn." This phrase means the person you are speaking to isn't as smart as you are but they are physically stronger than you are. You might hear this phrase in a movie where two characters have to go into a rough bar. The person who is the brains should do all the talking in the bar so they don't get into a fight. If they do get into a fight, then the person who is the brawn needs to beat up the attackers. Hahahaha :)