What specific characteristics distinguish an imperial stout from other kinds of stouts? My local growler shop regularly has a variety of stouts on tap, of which I usually pick Imperial. 

What, specifically, distinguishes an Imperial stout from other kinds of stouts (say a regular stout, an oatmeal stout etc)?
The first Imperial Stout was made by Thrale's Brewery to export to the Russian royalty, it had high alcoholic content so that it could survive the trip gracefully [1]. Since then Imperial has been used as a prefix to signify beers which are of higher alcohol volume than their normal variants, and luckily they're no longer just for Russian royalty.