Usually: Worn caliper hardware or loose brake pads shifting in the bracket.
But it can also be: Worn suspension components that only load up under braking, such as ball joints or strut mounts.
Clunk when you brake
Most of the time this is the brake pads themselves. Pads sit in a bracket with clips or shims to hold them steady, and once those wear down or rust, the pad has a little room to shift. When you press the pedal, the pad moves before it bites, and you get a clunk. Worn caliper hardware, the slide pins and bushings the caliper rides on, causes the same kind of noise. Neither one happens gradually. You just start hearing it one day.
The other possibility is something in the suspension that only loads up under braking, like a ball joint or a strut mount. These parts have some play in them all the time, but you usually only notice it when the car's weight shifts forward hard, which is exactly what happens when you brake.
How to tell which one it is
Find an empty parking lot and brake gently a few times at low speed, then a few times harder. If the clunk only shows up on the harder stops, or right as you first press the pedal, that points toward pads or caliper hardware. If you can also feel or hear a clunk over speed bumps, potholes, or when you turn the wheel while parked, that points more toward suspension. A mechanic can also grab the wheel at 3 and 9 o'clock and rock it to check for play in the wheel bearing or ball joints, which is hard to do reliably yourself without the car on a lift.
It's worth ruling out the cheap explanation too. A stone caught between the backing plate and rotor, or lodged in a wheel cover, can clunk on braking and nothing else. If the noise is inconsistent, comes and goes, or you can hear it more when turning slowly in a parking lot, check the wheel wells before assuming it's a part failing.
Is it safe to keep driving
A single clunk on brake application, by itself, is rarely an immediate safety issue. It's a sign something has worn past its proper fit, not that your brakes are about to fail. That said, worn suspension parts don't fix themselves and can get worse, so this is worth booking in soon rather than putting off indefinitely.
What the fix generally involves
If it's pad hardware, that's a straightforward job, usually part of a brake service, new clips or shims and sometimes new pads. Caliper slide pin issues mean cleaning and regreasing the pins, or replacing them if they're seized or worn. If it turns out to be a ball joint or strut mount, that's a bigger job and the cost depends on which part and how the suspension is built on your specific car. We'd want to put it on a lift and check things by hand before saying which one it is.