Diagnosis
That's usually the cooling fan for the magnetron (the part that makes the microwaves). Over time, the bearings in that fan motor can wear out or get gummed up with kitchen grease, causing a grinding or loud hum. It could also be the fan blade hitting something.
How to Fix It
1. Unplug it. 2. Remove the grease filter and wash it—a clogged filter makes the fan work harder. 3. If the noise continues, the fan is inside the top compartment. You'll need to remove the outer cover. Once inside, check for any debris touching the fan blades. 4. Spin the fan blade by hand. If it feels gritty, binds, or wobbles, the fan motor assembly needs to be replaced.
If That Didn't Work
A less common cause is a failing magnetron itself. If the fan is spinning freely and clean, but the loud buzz is coming directly from the large, heavy component on one side (the magnetron), it's likely the source. Magnetrons do eventually wear out.
Heads Up
That fan is critical for preventing the magnetron from overheating. Don't ignore this noise and keep using the microwave, or you could cause a complete and more expensive failure.