To clarify, I don't really like referring to games or gamers as hardcore. It has a lot of baggage implying pretentious elitists and what they do with their time.
However, as the other end of the scale beginning with Casual, it does have a use. Naturally it's subjective. I don't know why half the posts I've read equate this with being meaningless. There are a lot of things that are subjective and still useful as terms or concepts. I'm not very good at explaining what I take it to mean, but basically that it is challenging, it has depth, requires thought, knowledge and practice to play, and doesn't compromise these for the enjoyment of anyone who may want to play it without putting any effort in. While I haven't played Dark Souls 2 yet, Dark Souls definitely fulfills these criteria. For a start, the variety in builds and weapon sets make for an outstanding level of customisation and creativity. The level design was also (generally) very good, with places like Sen's Fortress having many traps that could be detected and avoided without death through observation (and then there's Lost Izalith which is a mess of bloom and tedious walking but we don't talk about that). The combat is physically challenging (and I've heard moreso in Dark Souls 2 with backstabs and ripostes being more difficult to execute and not getting I-frames), particularly with parry timing and against multiple enemies (for this reason Ornstein and Smough is one of the most exhiliarating boss fights I've ever seen), and as far as the plot and direction, it allows you to go basically wherever you can in the map and the information you get is from NPCs and can be cryptic. Another thing in its favour is the possibility of fighting in harder areas from the beginning, which is certainly a hardcore feature meant to appeal to veterans and those who like a challenge, although if you're only trying to progress through the game, the map doesn't leave a lot of question. Another huge thing is that there is a lot of content you could easily miss in a playthrough, so it takes exploration and thought to actually find all the content in the game. There is also quite high stakes for dying, the possibility of losing all your souls which are really the all-purpose agent of progression, but, with skill and care you can regain them.
That turned into essentially a mess, and was more about things in Dark Souls that are hardcore rather than what hardcore independantly is, but really I think that's the only way to do it. Just play the game and decide for yourself. There is so much variation in games that it seems silly to say "a hardcore game must have these things". And furthermore, games can have hardcore elements and casual ones as well, along with everything in between. For example, Dark Souls does not have a weighted inventory. I have little doubt that had it had some sort of item weight to every stone and arrow you can acquire and they opted to remove it in DkS2 there would have been a cry of casualisation, so that is a part of Dark Souls that does not require effort or thought. But there is a very clear distinction between Farmville and Dark Souls and I suggest that the people who play them are largely different markets. A remainder from another argument to ward off criticism, you can minmax in casual games, and you can employ strategy, but it still doesn't require the effort that it does to play harder games well, and if you didn't want to minmax, you could still progress anyway really without punishment.