The traction circle is way of thinking about the grip that a particular tire has on the road and how you can use it.
Visualize, if you will, a circle, with an x-axis and y-axis running through the center. The edges of the circle denote 100% utilization, the x-axis represents lateral grip (or cornering grip), the y-axis represents longitudinal grip (or braking/accelerating grip). This area in the circle represents the domain of your tire's grip. Points inside the circle are possible combinations of acceleration, braking, and turning; points outside cause the tire to lose grip and slide. If you're a real geek, you'll realize that this is a vector whose magnitude is always less than 1.
This traction circle is a way of teaching people the basics of tire grip, the essential limiting factor in performance driving. In the traction circle, you can be either turning left, turning right, accelerating, braking, or a combination of turning one way and accelerating and braking. Duh. The important thing the traction circle illustrates is that you can combine turning and speeding up or slowing down, but the less of one you do, the more of the other. This explains why you can't go through a hairpin at 100mph, but more importantly, it tells you why you can't go through a 51mph turn at 52. It also helps explain why turning strategies tend to tell you to brake, turn, accelerate rather than to brake through the turn, then accelerate through it.
It is also an important way of expressing driving cues. When a racer brakes at 80%, that 80% is not putting 80% of the pedal to the floor, nor is it a constant. The percentage depends on the overall size of the traction circle, which is the amount of grip available in the tire. If conditions change (such as cresting a hill or running over a bit of gravel), that 80% may become 110%, and the tire will slide. Of course, a racer's job is to always maximize available grip through a turn, so she would brake at 95% unless she was worried about weight transfers (which also affect available grip) or needed to turn.
Of course, the best strategy would be to follow very closely to the edge of the traction circle at all times so that one is not taken off guard by sudden changes, but you risk being passed by someone using 98% of their grip. Traction becomes an issue when following behind someone, as you will most likely be forced into the line they choose, so outbraking and pushing the car becomes the strategy to pass. However, because the difference between 100% and 95% is never more than a few seconds at the end of a race, it is more important to focus on cutting good lines and following the track than to focus on pushing the car.