We had this question the other day and I thought wow that is an awesome question. Most people just assume that it's just a good thing to have and really and that it is updated technology.
I found this picture on-line and I thought it was the perfect way to describe the difference between the two.
Without ABS in a hard braking situation you could slide and then possibly lose control of your vehicle. If you have ABS then your brakes will pulsate in a hard brake and allow you to remain in control of your vehicle.
Most vehicles are now equipped with ABS as a standard feature. For those looking for a classic or older model car this is something that you should ask about.