An EE is a bird that usually has a beard and muff, green or willow legs, a pea comb, and lays green eggs. But that is by no means set in stone. Basically, they are hatchery mutts, and they come with pea, bubble gum, or single combs, with green, yellow or slate legs, and they lay blue, green or pink eggs.
The reason they are called Easter Eggers is because they often produce eggs of various colors. They also boast an incredible range of plumage patterns. For many, that is part of their charm; there is no "variety" of chicken that is so variable. But they are nowhere close to breeding true; and so, as Anne rightly points out, they're not a breed, nor will they be for some time.
They are good, solid layers, usually, and they tend to be hardy. Onset of lay and other traits are too variable to pin down. Folks around here (rural Ohio) keep a lot of them, along with RIRs, as this makes a nice mix of eggs in the basket.