Personally, I've long been a fan of the term "extreme metal". It provides a nice, intuitive was to throw a net over a big chunk of the metal world and say "I'm talking about all this stuff over here." When I was first starting to learn about metal, I wish I'd been familiar with the term, because without splitting things into specific sub-genres or sub-sub-genres, it was often hard to find what I wanted. For example, searching "greatest metal bands" almost exclusively produced results like Iron Maiden and Black Sabbath. Those bands are great, but if you're looking for material from the aggressive end of the metal spectrum then such a search is of little use. A qualifier is needed. "Greatest extreme metal bands" provides a rather different set of results, which is handy if that's what you had in mind.
It's also a nice term because it allows you to talk about bands in a cross-genre way that might otherwise seem weird or lead to arguments over classifications. You may not be in the mood to argue whether Dissection is a black metal band or a death metal band or a blackened death metal band or a blackened melodic death metal band. Rather than invite that debate when you compare them to At the Gates, you can instead just discuss "extreme metal bands" and be done with it. Having such a broad term on hand can be very nice at times.
But what exactly is extreme metal? As I said before, it's a broad, intuitive term. That makes it, by its very nature, a bit hazily defined. Oddly, though, it was only recently that that lack of clarity really occurred to me.
See, I was driving to the store with the new Triptykon album blasting over my car stereo system (it's awesome, by the way) and I started ruminating on how Tom G. Warrior's involvement in Celtic Frost made him one of the most important figures in the history of extreme metal. Soon I started making a list of the top ten extreme metal bands in my head, mostly starting with revolutionary pioneers who got the ball rolling in multiple sub-genres: bands like Bathory, Sodom, Slayer, Venom, and Celtic Frost. Then naturally I started thinking about bands that were important mostly in their own specific branches of the metal tree, and suddenly I hit an impasse: I could not decide if Cathedral where extreme metal or not. My initial impulse was to say that they were, but when I really thought about it I couldn't say why exactly. After all, they were a doom band, and I tend to lump doom in beside thrash, black, and death metal in the extreme metal pile, but then again Reverend Bizarre and Saint Vitus and Witchfinder General are all great examples of doom bands that are clearly not extreme metal. Hell, even Black Sabbath can be considered doom, and if Black Sabbath fall under the "extreme" umbrella then it doesn't seem like the term is serving any purpose anymore.
So was the problem just that I was just wrong, and doom didn't belong within extreme metal at all? Well, no. I quickly reflected on Atra Mors by Evoken (which is also awesome, and which I finally got around to buying a physical copy of the other day) and concluded that doom could absolutely be extreme metal. So sometimes doom was extreme metal, and sometimes it wasn't.
Well there must be some criteria or quality that makes the difference, then. Could it refer to that metal that has primarily harsh vocals? That seems like the most obvious answer, but I have some issues there, too. Such a classification alone means that all sorts of -core bands that barely squeak through the door as being metal at all are suddenly all the way over on the "extreme" end, with heavy-as-hell metal bands with mostly clean vocals aren't. Personally, I'm going to take issue with any definition of extreme metal that includes Emmure but excludes Root. Besides, thrash is traditionally part of the extreme metal pile, and most of the key thrash bands didn't feature screams or growls on vocals.
As that last thought went through my mind, I suddenly hit a really major problem with sorting out this whole mess: what is Metallica? Clearly Metallica are a thrash band, and thrash is one of the big pillars of extreme metal, but can a band with dozens of radio hits actually be extreme metal? That sounds, if I may be a tad elitist for a moment, a little too mainstream to be labelled "extreme". On the other hand, you can't just exclude the biggest thrash band in the world purely because they're too successful.
And that's when I decided to drop the whole thing and walk away. Extreme metal, as useful a term as it is, doesn't have a proper definition. Some things are obviously part of its sphere, as I can't imagine anybody arguing whether or not Suffocation are extreme, but some things are just out on the fringes, subject to the whims of whoever is talking at the moment. That's fine, I guess. The last thing I want to do with a big blanket term is start fussing about all the nit-picky inconsistencies around the edges, since avoiding that very nitpicking was the main point in using it in the first place.
So that's extreme metal for you: it doesn't have a definition, but you know it when you hear it. Maybe.