For instance, you might say that the Fourier Transform is just a decomposition of a function of time into complex exponentials representing frequencies. But how does a complex exponential represent frequencies? Can you explain Euler's formula?
I usually pick someone I know well and consider what it would take to make them understand, given what I expect them to know already. I find this really helpful in testing my own understanding, but it's a good way of testing how complex an idea really is, relative to the average person's knowledge. (Incidentally I'd rank Fourier stuffs as pretty complicated, all things considered).