Usually: Low or old power steering fluid, or a failing pump.
But it can also be: On electric power steering, a failing motor or a fault the car has logged rather than anything hydraulic.
Groaning or whining when you turn the wheel
A groan or whine that shows up when you turn, and gets louder the further you turn, is almost always the power steering system working harder than it should. On most cars built before electric power steering became common, that means the fluid is low, old, or the pump itself is starting to go. Fluid that's low or breaking down doesn't lubricate and cushion the pump the way it should, so the pump whines under load. If the fluid's fine, the pump itself may be wearing out.
If your car has electric power steering — no hydraulic pump, no fluid reservoir under the hood near the steering rack — the noise usually points somewhere else. It can be a failing steering motor, or a fault the car's computer has logged that isn't a fluid or mechanical problem at all. Electric systems are quieter to begin with, so a new noise there is worth paying attention to.
Here's a check you can do yourself before anything else: pop the hood and find the power steering reservoir (skip this if you have electric steering — there won't be one). Check the fluid level against the markings on the side or the dipstick on the cap. If it's low, that's often the whole story, and it also tells you there may be a slow leak worth finding. If the fluid is full and looks clean, the noise is more likely the pump or, on electric systems, the motor or a logged fault.
Another quick test: with the engine running and the car parked, turn the wheel slowly lock to lock. If the groan rises as you turn and fades as you straighten out, that's consistent with the steering system under load — not a wheel bearing or CV joint, which tend to make noise that changes with vehicle speed rather than steering angle.
It's generally safe to keep driving in the short term, but don't ignore it. A power steering pump that fails completely can make the wheel suddenly much harder to turn, which is unpleasant at low speed and worse at higher speed. If the fluid is low because of a leak, driving on it longer just means more wear on the pump.
Putting it right starts with the fluid check. If it's just low, a top-off and a look for the source of the leak is the first step. If the pump is failing, it typically gets replaced rather than repaired. On electric power steering cars, a diagnostic scan to read any logged fault is the right starting point rather than guessing at parts. Cost varies a lot depending on which of these it turns out to be, so it's worth having it looked at rather than assuming the expensive answer.