I don't know much about output transformers. Can someone educate me a bit?

I have read an output transformer takes the signal from the tubes and transforms them into impedances and power suitable for your speakers. Seems like that wouldn't affect the tone much, but many people say the do.

So how much does an output transformer affect the amp's overall sound?

How do I know if an amp has a good one or not?

And what is a rectifier and what does it do?