I just read a very informative, if somewhat technical, article about transformers and why they are used in audio hardware.
If you are not an electrician, or don't have a background in electrical engineering of any shape or size, you may not know what a transformer even is. If I'm being honest, I have to think about it myself sometimes. And I had both digital and analog electrical engineering courses in college - though I now desperately which I had paid better attention at the time:-P. In my defense, the material never spoke to my needs, which at the time had to do with my band's PA system and our issues with feedback, etc.
Anyway, I digress as usual. In the most basic description, a transformer transforms things. Duh. But we're not talking about cars-into-robots here. It's about electrons. Those pesky electrons and how they flow (another simplistic explanation of electricity in general).
A transformer separates two electrical things physically. For example, instead of a single wire connecting two things - say a switch and a light bulb, you can stick a transformer in the middle of the wire. A transformer has two coils of wire inside it. If you had paid attention in your physics or EE class, you may have had a lesson in "induction." This means that an electrical current can be passed between two things without them even touching. Often this is demonstrated with magnets or even rubbing a rabbit fur on a plastic rod and then holding it over your head to watch it suck your hair to through the ether. This is a form of induction. One thing (a magnet or a charged rod) "induces" the current in something else (metal shavings, hair, etc.).
But why is that useful? Well, if you have some unwanted thing traveling along the first electrical portion, like a hum or something, you don't want to pass the hum along to the destination. So you can "de-couple" (a fancy way of saying "physically separate") the signals. But then how do you keep the desired power flowing? The answer is induction. The first coil of wire (remember the two coils thing in a transformer?), which is physically separated from the second coil, induces the signal to the second coil. This "air gap" (my term for understanding it) drops the unwanted stuff and only passes the wanted stuff along the circuit.
Now before the experts start hurling criticisms - yes, this does only describe one use of a transformer. You can use them for other things like transforming one type of electricity to another, useful for taking your hair dryer to Europe from the US. We lived in England for 4 years and had to have these heavy transformer boxes all over the house so we could plug in our American appliances.
Anyway, here is that article that speaks to how and why we need or want them in our audio gear. http://www.prosoundweb.com/article/making_it_match_an_introduction_to_transformers_in_audio_devices/