Brown sticker is a category of contract bridge conventional agreements defined by the World Bridge Federation (WBF).
Brown sticker conventions are considered, by some, to be difficult to defend against, and thus are only permitted at the highest levels of tournament play in most locations. Only highly unusual methods (HUMs) have a higher classification.
The official definition can be found on the WBF website[1].
A short summary would be that a convention qualifies for a brown sticker if it fulfills any of the following criteria:
Notable exceptions are the Multi 2 diamonds (due to its popularity), a natural 1NT overcall, and cue bids on strong hands to force partner.
The bottom line is, that if a bid is weak (or potentially weak having multiple options) and does not promise 4 cards in a defined suit (when weak) then it is likely to have a brown sticker.