Usually: The pads are gone and metal is running on metal.
But it can also be: A stone caught in the brake dust shield, which sounds similar but comes and goes.
Grinding when you brake
This is worth stopping for, not living with. Grinding when you press the brake pedal usually means the pad material is gone and you are down to metal on metal — the backing plate of the pad grinding against the disc. Every stop after that happens is cutting a groove into the disc itself, which is why this one turns into a bigger job the longer it goes on.
There is a cheaper, harmless possibility too. A small stone or piece of road debris can get caught behind the brake dust shield, the thin metal plate that sits behind the disc. That also grinds, but it tends to come and go, and it often changes with steering angle or shows up only at low speed, then disappears. Worn pads grind pretty much every time you brake, consistently, and usually on the same wheel or axle each time.
A rough way to tell them apart in a parking lot: roll forward slowly and brake gently a few times. If the grinding happens every single time, at any speed, that points to pads. If it is intermittent, or only happens sometimes and then stops, it is more likely something loose rattling around near the shield. Neither test is certain — it just narrows things down before you have someone look underneath.
Is it safe to keep driving? Short trips, carefully, probably won't strand you. But metal-on-metal braking means longer stopping distances than you are used to, and it is scoring the disc surface every time you use the brakes. If you can get it looked at in the next day or two rather than the next month, do that.
Fixing it usually means new pads at minimum. If the discs have already been cut into, they often need replacing too, since a groove in the disc surface will chew up a new pad quickly and won't brake evenly. If it turns out to be a stone or debris behind the shield, that can sometimes be cleared without replacing anything, though the shield itself may be bent and need straightening or replacing if that's what let the stone in.
Either way, we'd put it on the lift, pull the wheel, and look at the pad thickness and the disc surface directly rather than guess from the sound alone. Cost varies a lot depending on whether it's pads only or pads and discs, and by vehicle, so we would not want to quote that without seeing it first.