Originally named for the dope rocks that lie off the coast of Marshfield, MA. Later people used the branty rocks to try and compare super awesome stuff to it. For example, "This steak and cheese is awesome, kinda like the rocks off the coast of Marshfield".
Now it can be simply used as a synonym for super happy awesome fun things.
"Dude, thanks for being so branty and letting me slide on that $50 I owe you."
"Calm down, you're being very unbranty right now"