Resonator

Consider this article a stub while we wait for an official definition of what the Axe-Fx's resonator does.

This is a rough description of what a resonator can be:

I'm going to have trouble defining it without using other forms of the word. I also don't know how Cliff implemented it and there's a range of what resonators can accomplish. On the simplest end, it's like a peak EQ that emphasizes a particular frequency (think of how a cabinet is tuned to make certain frequencies kick). Getting more complex, it can be a bit like a reverb, but distinctly not a reverb. This can either give some body to an instrument (like adding the wooden box to a plucked string makes an acoustic, you can build some similar acoustic "simulations" with certain resonators) or just make it sound like you're listening to something through a pipe.

Pushing a resonator into less natural territory, it can add clangy metallic overtones or create a noise that approaches feedback or achieves oscillation at a particular (tuned) frequency. For a painful example of the latter, think of what happens when you leave a mic in front of a PA system. With minimal input, it will feedback at a certain frequency based on where the resonances of the system (mic, room, speakers) are. Those resonances can be artificially created by a resonator for some interesting ringing effects (and cut off before they fully feedback/self-oscillate).