The rise and fall of the magnetic fields acting on the metallic components. Ther is another reason but I will wait for someone else to explain.
Why does it hum? Because it doesn't know the words.

Bad joke, but I had to say it.
Think of a guitar string or any reed instrument that produces a sound; a note on the musical scale that the pitch is proportional to the frequency of the vibrating material.
The changing AC magnetic field causes the winding and core of the transformer or any other electromagnetic device (relay, contactor) to vibrate at a certain frequency. In this case, 60HZ or 60 cycles per second. If there is high THD involved then the pitch can vary because of the different frequencies affecting the fundamental. Pieces of insulation wedged between the windings and laminated core are used to supress the loudness of the hum (and for impulse level rating) but it still gets thru.
I had a customer that had a 20yr old 2500KVA dry type (GE) that produced a very loud hum.
(BTW the loudness is directly proportional to the loading; amount of current flow in the windings.)
This one was loaded to the 80% NEMA limit. Every PM period we would perform all the NETA tests but could not find anything wrong. Customer (TELCO office) was worried about the cost of the downtime ($1 million/ minute) if it ever faulted and finally had it replaced; mucho bucks!!

BTW another transformer, same size & vintage, in the power room did fail years later due to an internal fault. It was a nasty sight!
