After some digging on Q2A (the system the the Pokebase sections are built from), I found that the inner workings of the Q&A portions of the site use PHP and SQL, while the front end is handled by HTML, JavaScript, and CSS (which are standard for websites and browsers).
As for the database part of the site, the front end also uses HTML, JavaScript, and CSS, but I'm not sure what languages the inner workings would use, or if it's different from the Q&A portion. PHP and SQL are notable for being good at database management, though, so if I had to guess, I'd say those two are likely.