As Ninjamonkey described... overtraining is a product of training without allowing for proper recovery between workouts... at least that is the generally accepted definition... what he did is perhaps overdoing it or over loading, doing too much in one workout session... or perhaps attempting something which causes strain/injury... but I re-iterate that pushing hard in one session is not particularly a bad thing...
Pushing TOO hard is definitely a bad thing. Soreness and decreased performance for a few days tells me that he has overtrained. Overtraining isn't some mystical thing where you get ill and can't train, it can be something as simple as this but it can also go so far as to impair the immune system. To me, overtraining = excessive training that impairs results.
I would just like to make a small addition to the last sentance of your post... ... over a period of several workouts... I sometimes really push myself and that particular body part may hurt for several days (usually no more than 3 or so though) but I have in no way impaired my training or progress... just hit it hard for that work out to add a little shock to the system... but pushing too hard can be detrimental if its taken to the extreme... Also no one is implying that overtraining is mystical or that it makes you sick... it impairs results but I havent heard or seen anyone get sick from it yet...
Hmm, I don't remember saying it makes you sick, it can lead to injuries, is what I said. But the definition that we've been learning now is overtraining = pretty much what I've said before . I agree you can overdo it in one session, and it probably won't go down well, he probably won't get the BEST gains, but I wouldn't say it's overtraining, just a bit of overloading like shadow said, so as long as he doesn't do it again or too often, he's alright.