First things first, lets deal with semantics and the language police. In the context of beer, Imperial means, roughly, bigger. Double and Extreme mean, roughly, the same. So an Imperial IPA is a Double IPA is an Extreme IPA. These terms are all arbitrary. Now, the language police will tell you that imperial means related to an empire and that Imperial Stouts were so called because they were prepared for the Russian Imperial Courts. This is all true but guess what else is true? The American language is a living thing and when talking about beer, Imperial means bigger. I'm in ur language, bastardizing ur adjectives.
Now that we have that out of the way, it is useful to define an Imperial IPA in terms of what it is not. Trivially, an Imperial IPA is not an IPA, it must be bigger. But what happens if you just jack up the volume on the hops and the malt? Thats an Imperial IPA, right? Well, maybe not.
A bit of history is in order. At the turn of the 20th century (about 90 years before Boulevard invented beer, or something), Bass developed a high gravity pale ale called No. 1. This beer was effectively an English IPA brewed to a higher original gravity and with a commensurate higher level of hopping. Attenuation was fairly low (as is common for bigger beers) and the beer was left rich, heavy and somewhat sweet. This beer might have been been called Imperial IPA (if it weren't that American beer geeks did not corrupt the word until many years later), but it was called Barley Wine instead.
Fast forward to 1985. Ken Grossman's Sierra Nevada Brewing Company brewed one of the first extreme beers of the craft movement in the US (apparently following in the footsteps of Boulevard's Smokestack series, or something). This beer, of course, was Bigfoot the first American Barley Wine. Bigfoot followed in the mold of English Barley Wines except it was, generally, bigger and hoppier (and featuring American hop varieties). Since then many American Barley Wines have followed and they are all characteristically full bodied, malty sweet, extremely bitter, and featuring bold American hop character (unless aged).
So what happens if you, say, double both the malt and hops in a typical IPA recipe? You get an American Barley Wine, a style already named and established before John Maier coined the name "Imperial IPA" and before Vinny Cilurzo coined the name "Double IPA".
So how do you make a beer which seems like a big IPA but is distinct from Barley Wine? Vinny Cilurzo stumbled upon the formula by accident when he added 50% too much malt to his mash and compensated with 100% extra hops, creating the now famous Blind Pig IPA. The result is a beer that is bracingly bitter with huge hop character, but lacking the heavy body and sweetness of a Barley Wine.
So this was the mold for a while (and still is on the West Coast). A beer of about 1.080, with about 8% ABV. Pale gold to light copper in color, dry in the finish, drinkable (at least to the initiated). Hop bitterness was extreme, and hop flavor and aroma were as high as possible. These beers were not balanced, that was the point.
Since then the range of beers carrying the moniker "Imperial IPA" or equivalent have taken on a broader range that include higher alcohol levels, higher finishing gravities, and more residual sweetness.
I've found that beers labeled as such fall into roughly three categories.
1. Original Intent Imperial IPAs: These are of the West Coast type described above. Members of this category are Blind Pig IPA, Pliny the Elder, I^2PA, and Hop Stoopid.
2. Midwest Maverick Imperial IPAs. These are a newer class of beers seeking to make their own mark on the style. Characterized by higher gravity and alcohol than their West Coast Rivals, these beers are a bit fuller in body and with perhaps a bit of residual sweetness. They are not full bodied, they are not cloying, and they are not syrupy. Most importantly they remain drinkable by the pint, despite their alcohol, and they clearly feature hops both in bittering and flavor. Members of this category include Hopslam, Maharaja, and Double Wide.
3. Incognito Barley Wine Imperial IPAs. These beers are characterized by, well, being Barley Wines. American Barley Wines have no limit on hopping, so it is not a style that can be out hopped. What turns an IPA into a Barley Wine is sweetness, fullness on the palette, lack of drinkability and anything vaguely resembling balance. The archtypal example of this category is Southern Tier's Unearthly. Many "triple" IPAs are candidates as well, including a thoroughly enjoyable example from Moylan's. At their best, beers in this category are excellent but have more in common with Barley Wine than Imperial IPA. At their worst, they are cloying and uninteresting. It might be useful for breweries to market these as IPAs, but it is more useful for the consumer to think of them as Barley Wines.
So have yourself a Bigfoot IPA, or a Pliny the Barley Winey or pee in glass and call it Imperial Light American Lager (only if you had rice for lunch). I don't care.
Hopefully it is at least mildly useful to understand that not all Imperial IPAs are like each other, and some of them are suspiciously like Barley Wines. At the very least if you find that the only Imperial IPAs you really love are the impostors, you may want to check out Barley Wines. Conversely, if you find yourself drinking a fresh American Barley Wine and wish it were a bit smaller and easier to drink, go get yourself a Maharaja or Hop Stoopid.