What exactly is a Fighting Illini?

USC is Rose Bowl bound as the PAC-10 champion (for an unprecedented 6th year in a row). The Trojans will face the Fighting Illini.
This reality caused me to pause for a moment and ask, what exactly is a Fighting Illini? Is it multiple fighting Illinois students? Has anyone ever heard about the ferociousness of Illinois students? Should we be afraid? I wouldn't normally think so. Illinois seems like a pretty reasonable place. It's in the Midwest after all. I checked their official athletic website, and they don't even have a mascot as far as I can tell. We at USC have a great mascot: a guy in fancy clothes riding a Spanish Andalusian gelding named Traveler.

Returning to the original question, what is an Illini? The Illini can't use the excuse that all the good mascots were taken when they got around to picking one. That didn't stop the University of South Carolina from making idiots of themselves and choosing the fighting rooster as their fear inspiring idol.

Seriously. A rooster. Anyway, on January 1st, USC faces the fearsome...Illini. Couldn't they temporarily nominate a mascot, like the a muskrat? Maybe they'll throw some drunken fraternity brothers out on the field painted in orange. Projectile vomit, now that is fearsome.

Speaking of mascots, I finally figured out what a Bruin is...a baby bear. UCLA actually have a couple, Joe and Josie. Isn't that sort of arrangement illegal?

Update: According to http://members.tripod.com/~RFester/the Illini were the resident indian tribe in Illinois. H/t to Sue.