Diagnosis
That's the infrared LEDs for the night vision. On some units, the power supply for them can emit an audible coil whine or buzz, especially in a very quiet room. It's an electrical noise, not a mechanical fault.
How to Fix It
First, try switching the night vision mode. On the parent unit, tap the moon/sun icon to toggle between Auto, On, and Off. If the noise stops when night vision is forced Off, you've confirmed the source. The most common fix is to replace the camera's power adapter. Use only the original 5V/1A adapter that came with it. A different, even if it fits, can cause this noise.
If That Didn't Work
The noise might be coming from the parent unit's speaker amplifying very slight electronic noise. Try turning down the parent unit's volume all the way. If the whine stops, it's audio feedback. A firmware update might help—check VTech's website for your model and update via the app.
Heads Up
Don't try to open the camera to fix this. You'll break the weather seal and void any warranty. If it's unbearably loud and a power adapter swap doesn't fix it, contact VTech support—some early batches had this issue more severely.