An interval is the distance between two notes. Like a 2nd or a third. It's not the sounding of the notes.
Getting it from the horses mouth & hot off the presses, here's the definition from The New Grove Dictionary..., 2nd ed., 2001. Where I should have looked in the first place.
The simultaneous sounding for two or more notes. Chords are usually described or named by the intervals they comprise, reckoned either between adjacent notes or from the lowest... [and so forth]
The derivation seems to be from accord-> sounds in agreement. The opposite was once dischord, but we know chords can be discords nowadays, right?