Sconcing is a tradition at Oxford University of demanding that a person drink a tankard of ale or some other alcoholic beverage as a penalty for some breach of accepted etiquette. Originally the penalty would have been a simple monetary fine imposed for a more serious breach of discipline, and the word is known to have been used in this sense as early as 1617.
Minor offences for which a sconce might have been imposed included talking at dinner about women, religion, politics or one's work, referring to the portraits hung in the college hall, or making an error in the pronunciation of the Latin Grace.
The power to impose a sconce was not originally given to all present at a dinner. It might instead have been reserved for the person presiding on High Table, or perhaps the senior Scholar or other undergraduate at each table. Anyone feeling a sconce was deserved would be required to ask for its imposition (often in a "scholarly" language such as Latin or Ancient Greek). Should their request be granted a large vessel, usually full of beer, would be called for and the offender would have to attempt to drink it down in one go (perhaps while standing on the table). The amount of a sconce varied from two pints at Corpus, Oriel or Jesus, up to three and three quarter pints at St John's. Several colleges retain impressive antique "sconce pots" in their silver collections.
In the event that a person failed to drain his sconce, he was generally required to pay for the contents. It was also once relatively common for the sconced person to choose to share the contents of the sconce with their neighbours at table, thereby making amends to the "victims" of the original breach of good manners.
In modern times
Sconcing today is a phenomenon associated with 'crew dates', when typically a men's sports team and a women's sports team have a dinner together. Anyone at the table may stand and announce "I sconce anyone who ...". Those to whom the description applies must then stand and either take a drink or finish their glass. In this way it resembles the drinking game Never have I ever, but with different phrasing, and no requirement for sconces to proceed around the table.