To gain initiation into a criminal organization by competing a hit. Most common amongst street gangs and organized gang members.
Well Johnny you're almost an official member of the Gambino Family. To complete your initiation you must make bones: kill an Irish Mob soldier. Complete this, and under the authority as a Gambino Consigliere, the Family will welcome you with open arms.
To make bones about something is to cause trouble, start shit, or generally raise hell. Usually unnecessary.
"I heard you got in a fight with Richard."
"Yeah, we were having a good time and he thought we were noisy, so he decided to make bones about it.