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Tyres
So, we took a look at the effects of slip angle on a car tyre. This tells us about cornering forces. Percentage slip acts in a very similar way, but for longitudinal forces (accelerating and braking). Unfortunately, one of the fundamentals of tyre dynamics is that you can't get the maximum lateral (cornering) force out of a tyre at the same time as getting the maximum longitudinal (accelerating / braking) forces.
This brings us neatly onto ...
The Traction Circle
 The diagram shows a basic traction circle. The orange axis is longitudinal acceleration, and the green axis, lateral acceleration. Everything within the circle is theoretically available as a combination of forces from the tyre.
So you see that you can use the extreme maximum of the potential cornering forces from the tyre, as long as you make no longitudinal (accelerating / braking) demand on it. The white plot of the diagram shows an example of using the majority of the lateral forces of the tyre, which therefore dramatically reduces the longitudinal forces available.
This property explains why a rear wheel drive car can become "tail-happy" or sideways when you give it too much gas mid-bend. You effectively use so much of the longitudinal ability of the tyre, that the available lateral forces are reduced to a point where you are exceeding them, and the tyre will be saturated, and slide.
Taking this further, it explains why, as a general rule of thumb, front wheel drive cars understeer, and rear wheel drive cars oversteer.
The Contact Patch / Foot-Print
The contact-patch is the part of the tyre which is in contact with the road at any given time. This is where things start to get really interesting. The number of parameters and properties associated with what's going on in this small area are phenomenal, but we'll focus on the really important stuff.
 The diagram shows a simple contact patch. The orange line in the contact patch length, the green line, its width, and the hatched area is the contact patch area. Each of them has a different and inter-related affect on the performance of the tyre.
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