This phrase generally means homosexual,anal intercourse. This phrase finds it's origins in the 2006 release of Brokeback Mountain, a movie about homosexual cowboys. This is most commonly used as an insult between friends.
I bet you love gettin' it broke back style.
Engaging in anal sex with only saliva as lubrication.
I gave it to him brokeback style.
A description of Anal Sex generally between two males though not limited a male and a female, or two females (one of whom wears a strap-on phallus))
He walked into find Brad and Lisa going at it-Brokeback Style!