As American craft brewers, we have a reputation to uphold. Innovation, pushing the edge, leading the way for crafting excellent beers, and not just in realms that would leave the most steadfast observer of the reinheitsgebot in the leveling depths of despair either. We have been pushing the edge in many traditional styles as well, and in ways that would make traditional brewers of those styles proud, if a bit taken aback and even flattered. A great way to take a “traditional’  style and make it interesting is to “imperialize” it. This comes from the English tradition of brewing a malt and hop heavy version of their traditional stout for the Imperialist Czar of Russia. It became known as Russian Imperial Stout, and has since become a model for “imperializing” many other styles of beer. The label “imperial” applied to the label of a beer simply means a “stronger version of” as is stated in the history section of Category 14C Imperial IPA of the BJCP guidelines:

History: A recent American innovation reflecting the trend of American craft brewers
“pushing the envelope” to satisfy the need of hop aficionados for increasingly intense
products. The adjective “Imperial” is arbitrary and simply implies a stronger version of
an IPA; “double,” “extra,” “extreme,” or any other variety of adjectives would be equally
valid.

So imperial beers are simply stronger versions of their normal style counterparts, with more flavor, typically much richer, and much more alcohol. It is to be noted that the overall balance of the beer should be the same as the original style, but much more pronounced with stronger malt and sweet flavors being appropriately balanced by the desired hop aromas/flavors. With all the malt that typically can go into an imperial beer, it also leaves room for the brewer to experiment with new malts and flavors, thereby continuing the tradition of innovation we American brewers so proudly hold to.