[whatshisface]

Ok, let me guess without looking it up... A diffeomorphism is a smooth map that lets you switch coordinate systems.

(I sure hope that's not wrong.)

[auntienomen]

Pretty close. It's a smooth map with smooth inverse. If you've chosen chosen coordinates, it will transform them for you.

I think most physicists probably have a reasonable intuitive idea what a diffeomorphism is, since most have probably learned something about relativity.