Cats have disagreements. Diplomacy often fails to resolve these (if it's ever tried), resulting in physical altercations. Most of this involves a lot of swatting with claws. In fact, even a cat who has been de-clawed for years will usually instinctively slap you before he thinks to bite you (fortunately for my nose). They do bite each other, though (and me, too… sigh).
When they do bite each other, you usually don't have the big tearing lacerations that dogs open up on one another. Instead, you have small, but deep punctures. It's sort of the cat equivalent of getting shivved with an ice-pick. There's a little crushing, but not nearly so much as with a dog-bite.
Now you've got these very small (one or two millimeters) wounds, looking like baby Dracula paid a visit. They don't bleed that much, and the cat licks that off, and the fur covers up the scab. You don't see the wound (or feel it either, probably). Just think how long it takes to find Dracula's fang-marks on the naked skin of the beautiful girl's pretty white neck. And the vampire-hunters are really looking for something (unlike the cat-owner, who really isn't).
So the cat looks pretty normal… at first. BUT, since the wounds are about ten times as deep as they are wide, you can't wash them out, even if you did see them (which you didn't). You can't push a string. Fortunately, even though the wounds are contaminated with the evil germs from the attacking cat's mouth ("the germs that cause bad breath" and bad infections, too), the body's defenses usually take care of it.
When they don't, you may notice some tenderness, or pain, or swelling about three days after the wound. The bacteria multiply, damaging tissue, and the body's defenses come to the battle. The battle rages on, producing casualties: dead tissue, dead white blood cells, dead germs, leaking fluids… PUS, in short. This accumulation is painful, just from the pressure of the swelling, not to mention the dying tissue. This is an abscess, a pocket of pus. If you don't get your cat to his veterinarian first, the damage may deprive the overlying skin of circulation, and the abscess may break open through the dying skin. This is when you find some drainage. For instance, this cat put his head in the owner's lap, and she said, "What is THAT?"
As nasty as this looks, it's actually as bad as it's going to get. The overlying skin is all dead (Yes, I picked it off, primate that I am), and the pus has all drained away, and we just have some damaged tissue on the bottom. A little pain medicine, some antibiotic therapy, and some hot-compresses, and this will be closing up in a week or so.
It would have been better to catch this before it all got dead. Earlier (with just a little swelling), we would have made a small hole (as opposed to this huge one), drained the pus, irrigated the cavity, and started the antibiotic therapy. It gets better faster that way.