The roll centre is an imaginary, but accurately defined, point on the centre-line of the car around which the car rolls on its suspensions. The roll centre can be high off the ground, low, or even underneath the ground (it's only imaginary, remember). A line connecting the rear suspension roll centre with that of the front is called the roll axis. If the axis runs nose-down, the car tends to oversteer. If the axis runs nose-up, the car tends to understeer.The roll center of a car is where the car will roll (when cornering) when looked at from the front (or behind).
The location of the geometric roll center is solely dictated by the suspension geometry. The official FIA definition of roll center is:
"The point in the transverse vertical plane through any pair of wheel centers at which lateral forces may be applied to the sprung mass without producing suspension roll".
The significance of the roll center can only be appreciated when the vehicles center of mass is also considered. If there is a difference between the position of the center of mass and the roll center a "moment arm" is created. When the vehicle experiences lateral acceleration due to cornering, the roll center moves up or down and the size of the moment arm, combined with the stiffness of the springs and roll bars (sway bars in some parts of the world) dictate how much the vehicle will roll while cornering.
The geometric roll center of the vehicle can be found by following basic geometrical procedures when the vehicle is static:
Draw imaginary lines parallel to the suspension arms (in red). Then draw imaginary lines between the intersection points of the red lines and the bottom center of the wheels as shown in the picture (in green). The intersection point for these green lines is the roll center.
You should note that the roll center will move when the suspension is compressed or lifted, that's why it's actually an instantaneous roll center. How much this roll center moves as the suspension is compressed is determined by the suspension arm length and the angle between the top and bottom suspension arms (or turnbuckles).
As the suspension is compressed, the roll center will become higher and the moment arm (distance between roll center and the car's center of gravity (CoG in the picture)) will decrease. This will mean that as the suspension is compressed (when taking a corner, for example), the car will have less tendency to keep rolling (which is good, you do not want to roll over).
When using higher grip tires, you should set the suspension arms so that the roll center is raised significantly as the suspension is compressed.
Running parallel, equal-length suspension arms will result in a fixed roll center. This means that as the car leans over, the moment arm will be forcing the car to roll more and more. As a general rule of thumb, the higher the center of gravity of your car, the higher the roll center should be to avoid a roll-over.