The well is the shelf directly below the bar where a bartender keeps his house liquor. These bottles are kept where they are, partially to be easy to hand for a quick pour and partially to keep their labels out of view - most well liquors are cheap and unknown and most people at least like to harbor the illusion that they're not drinking stuff that comes in a plastic jug with XXX written on the side.
Quality of well drinks varies from bar to bar, of course, but it seems to be that the same few things hold true no matter where you go. House vodka is tolerable if mixed with something; house tequila will probably make you sick; house gin tastes like ammonia and smells like a Christmas tree (Just like real gin, come to think of it); and house whiskeys, over ice, ain't half bad, but I wouldn't recommend them neat.
The advantage of this stuff is that, at most places, it's cheap - it isn't uncommon in New York City, for instance, to find a $5 house shot and cheap beer (PBR, Rheingold, etc.) deal. Some places actually have real liquors as their house choice - Absolut, Jack Daniels and Cuervo seem especially common at these places, but their drink prices tend to rise as expected. Far as I'm concerned, any bar set up that way is probably not anywhere I'd like to spend a lot of time.