If your brakes make a squealing or whining noise, check the following:
Worn brake pads
Inspect brake pads. If they are worn or damaged, replace.
Brake pads vibrating
Inspect the brake pads.
There should be a metal gasket between the brake pad and the piston.
This gasket absorbs the vibrations that can increase in frequency to the point of squealing.
If they are missing, install new gaskets.
There are also anti-squeal lubricants that can be applied to reduce the squealing.
Badly worn discs
Inspect the brake discs.
If they are worn and or worn unevenly they need to be replaced.
Excessive play in wheel bearing
Inspect the wheel bearings and free play.
If the bearings have failed or worn then replace them.
Debris in calipers
It is possible that debris has been lodged in the calipers or between the brake pads and the brake discs.
Inspect the area and remove debris if required.