So...yeah. At least there's only three, right?
Like most of the characters and enemies in the God of War series, they take inspiration from Greek mythology, according to which, the Furies were the three goddesses of vengeance. There was Tisiphone, the avenger of murder, Megaera who represented jealousy, and Alecto, representing constant anger. Just who is seen in the trailer isn't yet clear. They were also mentioned in Homer's Iliad as "those who beneath the earth punish whosoever has sworn a false oath." See where this is going?
Given their origin of "beneath the earth," they're sent by Hades after Kratos swears off service to the God of war, Ares, which is where Ascension begins. It's been six months since Kratos has killed his wife and child. If he can kill the Furies, he can sever all ties with Ares.
Though the spider Fury is definitely intimidating, their traditional physical form sounds a little more like the famous gorgon, Medusa, which is described as having snakes for hair, and having blood dripping from their eyes. Since we've already seen this kind of appearance, you get that lovely spider-legged lady instead. Other depictions have shown them with the wings of a bat, and the body of a dog, so maybe that's what we'll be seeing next.
Given their importance, the Furies will more than likely be boss characters, and will pursue Kratos throughout the game. In written works, Athena has come to the defense of others that the Furies were after, so expect her to figure prominently once again.
God of War: Ascension will release March 12 in the US. A beta is also planned for release in November.