Why is my Laptop's battery charger is making a loud buzzing noise?

Most likely it is about to fail, and needs to be replaced , you can pick one up at any electronics place, noticed they were selling for E10 here, probably cheaper in USD.

I know what the problem is, but not how to explain it in terms that a non-electrician can understand.

Suffice it to say, your charger is bad, and should be replaced.

@jerv there is a 5 cent electronic component (that is a bitch to replace) that is dying, right?

@RocketGuy Comparing the cost of charger replacement to the hassles of repairing it, even having the skills to swap the parts in under two minutes isn’t enough to make dealing with it worthwhile. For those that lack the skills, even less so. Then again, I am a little biased since there are certain tasks I did too often in the past.

@RocketGuy ...I’ll speculate that the issue is a component in the circuit that detects power consumption and moderates the amount of power converted accordingly, probably a transistor of some sort maybe in an op-amp in a comparator circuit.
If that goes bad then the power conversion level may just go to maximum and turn the input transformer into a cranky electromagnet, hence buzzing.

And, yes, totally impractical to replace. If you have the chops you could open it up and prove out some theory of the cause of failure with your oscilloscope and DVM. But then you’re doomed to stare at it ruminating on the fact that if you could find a supplier for that failed component you’d have to buy 10,000 of them.

But if it’s a save-the-country/save-the-queen situation you might McGyver something together from parts ripped out of other gadgets. It will work just long enough for the Marines to storm Dr. Evil’s lair.