What Makes Up the Name: bro + romance
A bromance is when two grown-ass men share a special affinity, a bond that makes them almost want to make out, but not quite, because they're still scared of being called gay, because they're secretly gay, so they over compensate with rampant homophobia, which manifests itself with lots of jokes about homos and gays to each other so the other on doesn't think they're gay which they already know anyway. Or, it's just two guys who are way into each other and that's totally fine. Unless it starts to piss off your lady. It's also why this fight with your roommate won't last, so relax.
Origin: Listed in the NYT as a 2007 Buzz Word, but in usage before that time among bros and the bros who love them, bro.
See Also: broner, brodeo and The Onion's ultimate all things bro