A combination of the words "bro," and "obligation," used in such a manner to mean that it is a "bro's obligation."
Come on man, Jerry just got dumped. You know it's our brobligation to make him forget this night by giving him excessive amounts of alcohol, and/or taking him to the strip club!
Portmonteau of "Bro" and "Obligation". If you are bros with someone, no matter how shitty his band is or how mind-numbing his poetry is, you are obligated to be his number one fan. Or, you know, decide to take some time off from each other while you consider new bros that might be a better match for each of you.
"Dude, you read my book yet?"
"Naw man, haven't had the time."
"You got to make the time dogg. You've got a brobligation to fulfill!"
when you're holding up your phone and making faces at it, as though you are taking a selfie, but you're really taking a picture of the person across from you or the wall or anything else that seems interesting but you don't want to be caught dead taking a picture of.
This action is often made more convincing by wiggling the eyebrows or opening the mouth, to pretend you're trying to get a Snapchat filter to work.
FRIEND A: "Did you just take a stealthie of me?"
FRIEND B (turning phone around): "no I was just using snapchat's new filter, see?"