Trouble with List Category Template

Apologies up front. I am a completely ignorant guy tasked with adding new content to a site someone else set up originally. Another member of our organization was recently added to take care of adding some new content. He knows no more than I, and has somehow edited a template that showed each of our individual categories… I cannot figure out how to get it to work again. I’m not even explaining it correctly, I’m sure, but can someone help me figure this out?

The page I need help with: [log in to see the link]