A single click or clunk from the brakes - often right when you first press the pedal or let off - is a distinct noise from squealing or grinding. It usually means a part has a little room to move that it should not. Here is what causes brake clicking.
Loose pads shifting in the bracket
The most common cause is a brake pad with too much clearance in its caliper bracket. When you apply the brake, the pad shifts and seats with a click; releasing lets it move back with another click. This comes from worn or missing anti-rattle hardware - see brake anti-rattle spring and brake pad gap noise. Fresh hardware that holds the pad snug cures it.
Worn or missing pad clips
Abutment clips give the pad a clean surface to sit and slide on. When they are corroded, distorted, or were not replaced last time, the pad sits loose and clicks as it takes up the slack under braking. Rust building behind an old clip changes the fit and does the same - see when to replace brake hardware.
Sticking or loose caliper parts
A caliper that does not slide smoothly on its pins, or a loose caliper bracket bolt, can clunk once as it takes up play. Loose or worn slide pins are a common source - see sticking caliper symptoms. A bent dust shield tapping the rotor can also tick.
The fix
Most brake clicks trace to loose pads or tired hardware and are fixed with a fresh hardware kit - new clips, shims, and anti-rattle springs - installed on a clean, rust-free bracket, plus properly greased and torqued caliper parts. Fit quality pads with a complete hardware kit and the click goes away.