DIAGNOSIS That's typically the bake or broil element starting to fail. As the metal sheath develops a small crack or fault, electricity can arc internally, causing a loud buzz or hum that follows the cycling of the thermostat. It's most noticeable right when the element turns on.
FIX Identify which element is buzzing. Turn on the bake function and listen. Then try the broil function. Once you know which one it is (it's usually the bake element), replace it. The process is the same as for a dead element: unplug, remove screws, disconnect wires, swap it out.
IF THAT DIDN'T WORK A less common source of a buzz could be the oven relay on the control board sticking or chattering. If you replace the element and the buzz persists, the control board might be the issue.
HEADS UP Don't ignore this. A buzzing element is a sign of impending failure and can sometimes trip your home's circuit breaker. It's also a fire risk if the arcing worsens.