That's not so much of a breaker box as a dis-connect. Probably for the spa since it has GFI built in. Looks like a dedicated piece of equipment. You're probably going to have to run a wire from your main breaker box. You may be able to tie into an existing circuit to shorten the run, but I would definitely leave that up to a professional if you don't have any experience.
I'm not a licensed electrician but I have wired a couple of houses and done a LOT of do-it-myself electrical work.
*edit.
Turn on the spa then go flip the breaker in that box. I bet the spa will shut off.