Brain wine can be purchased from the shopping tab, or obtained by trading with other players. It appears in the Accessories tab as a green wine bottle with a brain on the label.
Brain wine is a consumable accessory that is used to upgrade skills. Brain wine, like skill books, may only be used once per skill, and only on skills that are below level 10 (not counting bonuses from exo gear and accessories). Thus no player can make use of more than 9 brain wines.
If you think you'll be using brain wine and/or skill books at some point, make sure to never raise a skill beyond level 8 using achievement points alone.
If you've already raised a skill beyond level 8 with achievement points (i.e., not using accessories or exo gear), you won't be able to use brain wine or a skill book on it. By using a skill reset (or two), you'll be able to lower your maxed out skill(s) down to level 8 and then apply the brain wine/skill book.