One of the reasons brakes make a grinding noise is their worn out. The brake pad material slowly wears away as you drive. If too much of the pad wears away the brake rotor will contact the backing plate of the brake pad. When this happens, it starts to make a grinding noise. Premature failure of the brake pads can be caused by a bad or sticking brake caliper. Inspecting and lubricating the brake calipers and brake caliper brackets prevents premature brake pad wear. If a problem is found during the inspection the brake caliper and brake caliper bracket needs to be replaced.
The picture shows that the brake pad is starting to separate from the attachment plate.
Another reason your brake pads could be making a grinding noise is from a hard item in the brake pad itself. Brake pads are made of many different ground up items including metal. Sometimes the pieces are not ground up properly and they can cause a grinding noise. When this happens the best thing to do is replace the brake pads and resurface the rotors. If replacement is not an option there are "Brake Quiet" products that can be put on the face of the brake pad to help quiet it down.
A third reason for a grinding noise is rust on the face of the brake rotor. Rust can form on the brake rotor from many things. One of the most common is from parking outside while it is raining. The rain splashes on to the brake rotor causing rust. When the car sits for a while rust can form on the rotor. This rust can cause a grinding noise and it usually goes away after a few stops.
Surface rust on the rotor face. This rust will go away after a few stops
If your brakes are making a grinding noise it is best to have a professional mechanic perform a brake inspection on your car.