Daria: As far as I can make out "edgy" occurs when middlebrow, middle-aged profiteers are looking to suck the energy--not to mention the spending money--out of the "youth culture." So they come up with this fake concept of "seeming to be dangerous when every move they make is the result of market research and a corporate master plan".
- Daria, Episode [3.05] The Lost Girls.
Edginess refers to people trying too hard (and sometimes too aggressively) to make things more tragic, grimdark, controversial or cool in how they go about things. Generally used around these parts as a negative adjective. Has no relation to Hunter: The Reckoning.
Edgy people usually can be discerned by their senseless insistence on driving a vague argument or scenario to its darkest possible outcome and openly expressing their disdain at rationalizing villains or finding a middle ground in discourses, insistently pointing out why insignificant characters should be ignored because life itself is meaningless.
This is not to say that said elements are bad in of themselves, but rather that their sloppy execution is. Edgyness is in some ways like a cargo cult. During WWII in the Pacific, the US military set up bases on remote, but inhabited islands, bringing with them a lot of stuff like planes and cars and so forth that was quite amazing to the stone age natives, to whom the world had been a few dozen square kilometers of land surrounded by ocean, with hazy stories of other such islands. When the military left, some of the natives took to making coconut and wooden radios and flight towers based of some hazy recollection of the military variants, unaware that making the shape does not get you the actual thing. Likewise, someone of (at best) mediocre creative abilities sees some fiction that makes good use of melodrama, gritty settings, dark humor and such, made by people who know what the hell they're doing and figures "I can do that!", leading to said person haphazardly applying those elements incorrectly. The results of such efforts are either tiresome, unintentionally funny or just painful. This is stereotypically prominent/popular among teenagers all too eager for "adult" things (eg: violence, sex and so forth in their limited perception born of denial, rather than complexity, subtly, nuance and some actual understanding of the human condition) and those individuals who pander to said demographic.
Another and somewhat less negative use of the Term is to describe something which is being on the edge of what's acceptable and pushing established boundaries of convetion. If one wanted a positive example of this, one could argue that Batman: The Animated Series was Edgy for making an animated series which defied expectations of what a such a series could do with a dark tone. A more direct example of this would be Ren and Stimpy (which was crude and vulgar) or Invader Zim (which could get get dark in subject matter and used a fair bit of black humor) and a decent bit of the comedy was of the "I can't believe that they'd did THAT on a kid's cartoon show!". It can work but A: if you do it enough the boundaries shift and what was edgy becomes the new norm and B: there is always the risk of falling over the edge.