If you're lucky, ABS will just stop working. In this case, your car will continue to function as normal, but without the benefits of ABS. You'll have to be extra careful when braking, especially in wet or icy conditions.
If you're not so lucky, the wire break can cause your car to lose control. This is because the ABS system is responsible for modulating brake pressure. Without it, your brakes will lock up more easily and you could skid out of control. If you're driving at high speeds when the wire breaks, this could be particularly dangerous.