Before this gets really confusing, let me make it as simple as I can. In oval racing, obviously we all only turn left all of the time. This means we don't really need to worry about how well the kart handles turning right. So stagger helps us turn left by having one tire larger than the other. In our case, the right tires are larger than the left tires. Stagger is the difference in circumference/roll-out between your left and right tires.
How it works as simply as I can explain it.
Calculation: Right Tire -- Left Tire = Stagger
First off, front stagger does not have much of an effect unless you miss it by a country mile. You will most likely feel very little difference in 1" of front stagger vs 1.25" of front stagger. Because the front wheels turn independently, stagger is basically a moot point other than making sure the body isn't dragging.
Rear stagger is where the rubber really meets the road for stagger in karting. Because we run solid axles, the axle always turns both tires at the same rpm. When we introduce stagger to it, the right side tire is larger than the left. The larger right tire forces the rear axle to roll similar to that of a Dixie cup. If you don't know what I mean by that, take just about any foam or plastic cup, tip it on its side and roll it forward. It will roll in a circle. Stagger does the same thing.
In practice, stagger can help you turn. Generally speaking the smaller the track the higher the stagger. Stagger will help you turn, but if you have too much, it can slow you down on the straights because of the kart being bound up with itself. All chassis manufacturers publish their baseline stagger numbers for your setup. Find what your chassis manuf. says and start there. If you have multiple sets of tires, make one smaller, one on the numbers, and one larger just to try it and to feel the difference.
I hope this is clear enough. I know for a fact this thread will become very confusing as the day goes on.