The term "imperial" was used in the 1800's for beer (usually stout) that was brewed in England but then shipped to Russia - specifically the imperial court of Russia! Brewers later started using the term more generally to indicate their top-of-the-line luxury beers.
With beers coming from American craft brewers these days, "imperial" is an indication that the beer is going to be big and bold regardless of the style. The hops and malts used during brewing are doubled or even tripled, and the resulting beer can pack quite an alcoholic punch ranging from 8% to 12% ABV.
These beers are definitely worth a try whenever you see them. If you like the basic style (stout, IPA, etc.), chances are that you'll enjoy the amped up imperialized version as well. They go well with rich, strongly flavored foods, and they make an excellent after-dinner sipping beer. Because they're so high in alcohol, one or two is usually our limit!
A few good ones to try are Left Hand's Imperial Stout, Dogfish Head's 90 Minute IPA (or 120 Minute IPA, if you can find it), and Rogue Ale's Imperial Pilsner.
What imperial beers have you had recently?