Usually: A failing belt-driven pulley or tensioner bearing.
But it can also be: On an automatic, a transmission whine that rises with road speed rather than engine speed — which is a different and more serious thing.
Whining that gets louder as you accelerate
Most of the time this turns out to be a pulley bearing or a tensioner going bad on one of the belt-driven accessories — the alternator, power steering pump, or A/C compressor. Those parts spin faster as the engine revs, and a worn bearing inside one of them makes a whine that rises right along with it. It's a common failure and, as these things go, not an expensive one to put right.
But there's a second possibility, and it matters that you tell them apart before anyone touches the car. On an automatic transmission, a whine that rises with your road speed rather than your engine speed can point to something inside the transmission itself — a worn gear set or a failing pump. That's a bigger job, and it doesn't share a fix with a bad pulley.
How to tell which one you have
This is the single most useful test you can do yourself, and it doesn't cost anything. Find a safe, flat spot — a parking lot works fine, or a quiet stretch of road with no one behind you. Get the car moving, then shift into neutral and let it coast while you press the gas pedal a little, letting the engine rev without the car actually speeding up.
If the whine rises and falls with the engine RPM, even though the car isn't accelerating, it's almost certainly the belt-driven pulley or tensioner. If the noise stays flat no matter what the engine does, but changes when the car's actual speed changes, that points toward the transmission. Either way, remembering which one it was — and telling whoever looks at it — saves a lot of guesswork.
Is it safe to keep driving
A failing pulley bearing can usually be driven on for a while, but "a while" isn't forever — if the bearing seizes or the belt comes off, you can lose your power steering or your charging system with no warning, which is a bad time to find out. A transmission whine is worth getting looked at sooner rather than later, since ignoring it tends to turn a repair into a rebuild.
Either way, this isn't something to ignore for months, but it's also not something to panic over. Get it checked in the next week or two.
What the fix generally involves
If it's the belt-driven side, the shop pulls the belt, spins each pulley and the tensioner by hand to isolate which one is rough, and replaces the bad one — a job that's usually done same-day. If it points to the transmission, that starts with a proper diagnostic before anyone talks about parts, since the range of possible causes — and the cost that comes with them — is a lot wider.