Oisin Tymon is one of the producers on the show, and has been for some years. Clarkson apparently (according to newspaper reports) screamed at him for quite a while because his hot dinner wasn't on the table when he arrived back very late, and then punched him.
Tymon did nothing about it; he turned away and went to the A&E (ER in American) and got himself checked out, as you always should in case of concussion if you have a blow in the face.
Clarkson then tried many times to contact him and apologise, and then went and reported what he had done to his bosses.
He was on his last warning, and so was suspended while there were discussions, and then his contract was terminated.
Oisin Tymon behaved perfectly, doing nothing to make the situation worse, making no report of the assault; he is now refusing to press charges.
It says something about Clarkson's fan base that Tymon is now getting death threats and being mocked on Twitter.