The stability system is basically an addition to your abs brake system. It operates by adding additional sensors such as a steering wheel position sensor and a yaw sensor and is designed to determine if the vehicle is losing directional control.
It can apply braking to specific wheels in an attempt to correct if the vehicle is sliding or losing traction.
If the stability system light is on, then the system is disabled for a failure. It can be disabled for several reasons.
If the abs light is NOT on as well then it is likely not a wheel speed sensor failure. It can be a steering wheel position sensor or yaw sensor. It can also be disabled due to an engine control fault such as a misfire that will disable traction control.
Do you have an abs light on or check engine light as well? If not, the most common cause is generally the steering wheel position sensor.
However I would recommend having the system scanned for fault codes so at least you know exactly what part of the system the failure is in.