8/10th, 10/10th etc...
 

What does this mean exactly?

Is there a mathematical formula, or a strict definition of what driving at "10th's" is?

No. It is a subjective criteria for describing how hard you're pushing a car, and it's about as scientific as someone saying they're 'taking it easy' or 'driving like crazy.' I guess anything less than 10/10ths means that the driver feels he was still leaving some time on the track, usually because he wants to imply he didn't want to spin or crash.

It's also often used as an excuse for lousy lap times. ;)

Put it this way, 11/10 = into the armco :)