Usually: The wear indicator on the brake pads.
But it can also be: Glazed pads, cheap pads, or just moisture on the discs first thing on a damp morning, which stops after the first few stops.
Squealing when you brake
The most common reason for a squeal under braking is the wear indicator built into the pad. Most brake pads have a small metal tab that touches the disc once the friction material wears down to a certain point. That tab is designed to make noise. It is not a sign that anything has broken. It is the pad telling you it is getting close to the end of its life, and it is a much cheaper problem to deal with now than in another few thousand miles.
That said, squealing is not always the wear indicator. Glazed pads can squeal too. That happens when the pad surface gets overheated and hardens, often from a lot of stop-and-go driving or riding the brakes down a long hill. Cheap or low-grade pad material can also squeal even when there is plenty of pad left. And on a damp or cold morning, a light coat of surface rust or moisture on the discs will squeal for the first few stops and then quiet down once it wears off. That last one is harmless and costs nothing to fix.
How to tell which one it is
Pay attention to when the noise happens. If it only shows up on the first few stops of the day, especially after rain or overnight dew, that points to moisture on the discs and nothing more. If it squeals every time you brake, warm or cold, dry or wet, that leans toward the wear indicator or glazed pads. You can also look at the pad through the wheel spokes on most cars. If the friction material looks thin, under a quarter inch or so, that backs up the wear indicator explanation.
Is it safe to keep driving
Yes, in the short term. A squeal by itself is a warning noise, not a sign of reduced stopping power. Keep an eye on it and don't put it off for months. If the squeal turns into a grinding or a deep metallic sound, that usually means the pad is worn through and metal is contacting metal, and at that point it needs attention right away.
What fixing it involves
If it's the wear indicator, the fix is a pad replacement, and a shop will usually check the discs at the same time since they wear together. If the pads are glazed, sometimes resurfacing the discs and replacing the pads solves it. If it turns out to be cheap pad material, swapping to a better pad usually clears it up. Cost varies quite a bit depending on the vehicle and whether the discs need to be replaced or just resurfaced, so it's worth having someone look at the actual wear before assuming which repair you need.