I started my car and the anti brake light came on and stayed on. What does that mean? It went out when I shut off my car.

This means the ABS is not working. However, the conventional braking system is working.

On each wheel that is equipped with ABS (front two wheels and rear wheels if they have discs), there will be an ABS ring in the wheel bearing which has magnets inside it and an ABS sensor on the hub measures the distance or time in between the magnets and it knows when you've hit the brakes or what speed you are doing and so on. The light on the dash could possibly mean that ABS ring is worn or dirty, the sensor is worn or dirty, a frayed cable, or the master plug may have came loose which means there will be no signal sent from the sensors causing the light to come on.

Check fuses ,wires ,sensors and connector for loose or damage if good have vehicle scanned for trouble code sum auto stores such as auto zone-advanced auto do it for free is ur starting spot the code will tell u what sensor or unit is causing problem