What's the purpose of anti-lock braking systems?

It's easier to move an object with wheels because the friction (static or kinetic, but probably static) is not opposing the motion of the vehicle, it's only opposing the forward motion of the bottom of the wheel. The very bottom part of the wheel never moves forward at all in non-skidding rolling. The wheel gets "around" friction by moving the part of it that isn't in contact with the ground.

Rolling friction is the combined effect of forces that oppose the rotation of the wheel. It includes friction in the wheel bearing (the part that attaches the rotating wheel to the non-rotating axle, usually designed to minimize friction). It also includes tiny non-elastic deformation of the wheel where it meets the ground. (That effect can be seen in an exaggerated way if your tire pressure is low.)

So how can you stop your car if rolling friction is low? Increase the rolling friction. When you apply your brakes, the pad presses into the disc or drum, creating friction - rolling friction because it becomes part of the forces that oppose the rotation of the wheel.

You still need static and/or kinetic friction because rolling friction is an effect between the car and the wheel. You additionally need an effect between the wheel and the ground to actually stop the car. If you were driving slowly on perfectly frictionless ice, and you put the car in neutral, the wheels would stop spinning in maybe a minute because of the rolling friction, but the car would keep moving. If you put on the brakes, the wheels would stop spinning almost instantly and the car would keep moving.

If you had ABS, it would kick in and disable the brakes, but it wouldn't help because normally it's the friction with the road that starts your wheels spinning again after they lock. There would be no friction with the ice to start them moving again. In reality ice is not completely frictionless, so ABS might help on ice still.

Rolling friction is what allows you to steer the vehicle. If the wheels are locked up, the kinetic friction is much greater than the rolling friction and the vehicle skids out of control - turning the wheel essentially maintains the same contact patch which has no significant effect on turning the vehicle.

Static friction is essentially what holds the vehicle on a hill when the brakes are applied.

ABS brakes apply the brakes and releases them many times faster than the operator can to provide both kinetic and rolling friction to allow the driver to maintain control in a panic stop.

I've had both. The anti-lock brakes definitely stop faster. Especially in snow, if you lock your brakes, you're sliding and barely stopping. Anti-lock brakes perform better.

Kinetic friction between two materials is USUALLY smaller than static friction. Their are some rare material combinations where this is not the case.

"If kinetic friction is really smaller than static friction, then why is it easier to move an object with wheels, versus and object that has no wheels?"

The wheel has the least surface area making contact with the ground, meaning least impact of friction.

You also have to consider that with anti-lock brakes, it's the pad touching the wheel that slows the car, vs. without anti-lock brakes, it's the wheel making contact with the road that is stopping the car. The friction experienced between these two is different, and with anti-lock brakes it's more friction.

The theory behind anti-lock brakes is simple. A skidding wheel (where the tire contact patch is sliding relative to the road) has less traction than a non-skidding wheel. If you have been stuck on ice, you know that if your wheels are spinning you have no traction. This is because the contact patch is sliding relative to the ice (see Brakes: How Friction Works for more). By keeping the wheels from skidding while you slow down, anti-lock brakes benefit you in two ways: You'll stop faster, and you'll be able to steer while you stop.

The point of anti-lock breaks is to stop the car as quickly as possible without the car skidding. (I'm going to leave out the different types of friction so I don't confuse you) When the brakes are fully applied and a car starts to skid, you have to wait until that car stops skidding in order for the brakes to work again, but this usually doesn't happen before you hit a tree or go off the road).

With anti-lock brakes the computer controls the force on the brakes so that the tires are always rolling, if the car starts to skid then the brakes release really quick to allow the tires to roll.(The chatter back and forth very quickly) By allowing the tires to roll you can now effectively put all your braking power into stopping the car without having to wait for the car to stop skidding.... Hope that helps

I take it you're not a driver. It becomes pretty clear when you are. Basically if you're driving a car without ABS and you have to stop suddenly, the stopping of the wheels provokes a slide because of the weight of the car (kinetic friction). So in order to stop, you have to pump the brake - the initial braking (static friction, if only for a fraction of a second) slows you more than a continuous slide. Pumping the brake slows you much, much more quickly. Stop - slide - stop - slide is better than stop - slide all the way to your target.