
The camber angle is the angle at which your tires lay relative to the vertical axis of your car. Assuming your chassis is level, it is also the angle at which your tires lay relative to perpendicular to the ground. A tire that is perfectly parallel to the chassis' vertical axis (and thus perpendicular to the ground) is said to have zero camber, whereas tires angled inwards towards the chassis are said to have negative camber. Camber is one of the most important aspects of an alignment because it greatly affects tire grip.
Shown here, a car with negative camber:
The basic concept of camber importance is that a tire makes its peak grip when it is perpendicular to the ground. Here is a graph, showing this:

Thus it is the suspension geometry's task of keeping the tire as vertical as possible over the widest variety of conditions. Unfortunately, that's rather difficult to do because a car's chassis moves (rolls and dives) as it goes over bumps or around corners. The suspension geometry cannot change camber as quickly as needed to compensate for body roll, since the tires (which are attached to the chassis, obviously) also roll during body roll. Thus, if the car's suspension geometry does not alter the angle of the tire relative to the chassis, the tire itself will go off-camber and lose grip.
Here is a diagram showing this phenomenon for a Mazda6 and a Mazda 626. The straight line graphs body roll, while the two curved lines show the amount of camber change seen during body roll. Notice that camber change does not happen nearly as quickly as body roll. Also notice that the Mazda6, which uses double-wishbones, has a camber curve that accelerates as it progresses, unlike the strut-based Mazda 626:

Race cars deliberately run several degrees of negative camber. Part of this is because camber curves do not keep up with body roll, but there is another handling change that can be desirable. A tire with camber always wants to turn. Here is a graph showing the extent of which camber improves turn-in:

What this shows is that a tire generates lateral thrust (steering) just from having camber. Thus, camber improves steering response because the tires always want to turn. The moment you put more weight on a tire, the car is going to turn because the tire was already trying to do that.
However, this is also why stability goes downhill with lots of camber. Your tires will continually fight one another for grip; each trying to turn inwards while you fight to keep the car straight. It's going to feel almost like running lots of toe-in up front. However, since your tires are fighting one another instead of working together, you will lose straight-line grip. This is seen in the previous graph: your grip under braking will drop rather considerably with lots of camber.
To help gain camber while steering but not while braking, cars angle the axis at which the wheels steer. This creates what is known as dynamic camber. One cause of dynamic camber is known as the steering axis inclination (or SAI). The SAI is primarily used to create a low scrub radius (which improves steering feel), but a high SAI will cause a camber change away from the direction the wheels are turning. This is not desirable. However, the other contributor to dynamic camber- known as the caster angle- does cause a camber change in the direction of the turn. Cars with a lot of caster will visibly angle their tires into a turn (more so the sharper the turn) while having relatively little or no camber with the wheels pointed straight. Caster also creates a stronger self-centering effect from the steering wheels.
So you can see, there are many factors that influence camber. If you find that your tires are wearing faster on the outsides than the insides, that is a good indication that you need more camber. Even more accurate would be a temperature probe to tell you which part of the tire is doing the most work and thus creating the most heat. Just beware the trade-offs: if you find yourself needing many degrees of negative camber at rest just to get even tire wear, you are starting to deteriorate your braking distances, perhaps rapidly.
Having ideal camber at all times is an impossible task, but good compromises can be made. The goal of suspension tuning is to find the best compromise, and that best compromise will vary widely depending on the car's use or driver's preference.