To drink an alcoholic beverage while is still in the brown bag supplied by the seller. Reasons to do this include, but are not limited to: discreet drinking, hiding of girly drinks to avoid embarrassment, to get more drunk than would be socially suggested (by hiding harder liquor), and to promote humor value of drinking. Can also suggest bringing alcohol to a party as to have an alternative to undesirable beer.
"Dude, I just got a keg of Natty for Saturday. You gonna come?" "Sure, but I'll be brown bagging it though."
"Hey, you brown bagging a Zima over there, or what?"