The well is the shelf under the bar where they keep liquor at hand for mixing drinks. So, a well brand or house brand is the brand of liquor served when a customer requests a drink by its generic name (e.g. gin and tonic, scotch and soda). It's usually the least expensive brand served, as opposed to more expensive call brands.
Well is used instead of really nowdays because people who speak english correctly are considered to be un-cool by chav idiots, it used to be only used by such idiots but now they've ruined the english language for a lot of other people and decent people have started saying it. The correct way to use the world well is at the start of a sentance.