Ah, just the kind of question to start out with.
We don’t actually know much about them, to be perfectly honest.Most of what we do know comes from sources like Rose or Feferi, who could be misled by the Dark Gods in question, or Doc Scratch, who could be misleading US. Let’s take a look at what we DO seem to know.

First of all, the Horrorterrors, or the Dark Gods, exist beyond Derse, beyond the Furthest Ring, in the space between different sessions. They seem to be a “part” of the game, though this is a tad bit dubious. Either way, in the two sessions we have seen so far (the kid session and the troll session, if that wasn’t clear), they have functioned as an aid to the Derse Dreamers, much like the clouds of Skaia aid the Prospit Dreamers. They set up the dream bubbles in the Furthest Ring at Feferi’s request, to allow the living and the dead to communicate through dreams and memories. See this flash: http://www.mspaintadventures.com/?s=6&p=004748 That also establishes two other important things, the first being the link between the Dark Gods and the Squiddles. The suiddles are associated with the Dark Gods and the Horrorterrors use them as a kind of relay between themselves and people who don’t want to look at eldritch abominations. The second thing about this flash is when Dave takes off his shades, more on that later. They took a very active role in Rose’s development throughout the game.

We all remember how that turned out, yes?
They led her to discover the Green Sun and what it did, telling her to destroy the book with the genetic code for the first guardian in it (still not sure what the point of that was, since causality dictates that Bec HAD to come into being somehow, unless the Dark Gods are trying to fight against the very nature of paradox space, which may or may not be part of the MO, as will become apparent), and led to the entire plan to destroy the Green Sun using the Tumor. This is all apparently in hopes of stopping the Horrorterror from being “massacred.” This ENTIRE conversation between Rose and Dave is very illuminating: http://www.mspaintadventures.com/?s=6&p=004937 To summarize, something is out in the Furthest Ring killing the Horrorterrors, and they’re asking Rose and Dave for help. This “help” consists of blowing up the Green Sun using the tumor. They make the map to the Green Sun, the kids blow the thing up. Presumably whatever is killing them is powered by it.

We thought it was that guy for a long time, with Lord English making a close second.
…At least, that was what we thought for the majority of Act 5. Cascade sorta threw that for a loop. We find out that the Tumor in fact CREATES the Green Sun. The Dark Gods helped Dave make the map through space AND time, so they must have known that when they arrived at the location of the Green Sun, there wouldn’t be a Green Sun. So are the Horrorterrors working with Lord English and Doc Scratch? Hard to tell, especially once we saw LE’s peg leg. Remember that link to the squiddles I mentioned? They get killed too, by a pirate named Skipper Plumthroat (check out the Squiddles Album for more haunting lyrics on that subject). LE’s peg leg seems to indicate a link to this Skipper Plumthroat, so LE could be the one murdering all of the Horrorterrors. That’s all speculation, mind you. It’s probably worth it to bring up again the burning of the First Guardian Genetic code that the Dark Gods made Rose do. It’s possible that the Dark Gods are far from infallible, and know a lot less than their eldritch forms would have us believe. They thought they could stop their massacre by burning the genetic code, they thought they could stop their killing by blowing up the Green Sun, and they thought they could stop Noir by making Rose go grimdark to take him on. But all their plans fail because they have a lot less omniscience than beings with the label “Dark Gods” may be believed to have. Again, that’s just speculation.
One last thing I want to touch on. I just mentioned Rose going grimdark. See this short flash: http://www.mspaintadventures.com/?s=6&p=005539 Rose is angry that she has let her mother die while she was off on the errands of the Dark Gods. Scratch then tells her to consult the all knowing cue ball as to just what the deal is with the Dark Gods, leading to that flash. Just to infer, it seems that this is a kind of trigger. There’s a couple ways to interpret that trigger. Either seeing the answer itself causes her to go grimdark, OR (and I find this to be the more likely option, but you can decide that for yourself) the Dark Gods saw that if Rose saw the answer from the cue ball, they would lose control of her, and so they completely took over in retaliation. Just another event that completely muddles trying to figure out what the Horrorterrors’ true intentions are.

And don’t even get me started on this image.
Like I said at the beginning, there are a lot of unanswered questions about the Horrorterrors. We do have a some information, untrustworthy as the sources may be, so we can make some educated guesses at least! I hope this helps to understand just what role the eldritch abominations that live in the Furthest Ring play in Homestuck!