What does a person do in the job of speleology?

Study scientifically caves and their natural contents. It's an umbrella term for a range of scientific disciplines.

I don't know that there professional speleologists per se, but many of the studies are carried out by people who are geologists, biologists etc as an extension of both their work as scientists and their hobby of caving!

Some studies though are important beyond simple scientific curiOSity. For example the learned journal 'Cave & Karst Science' sometimes publishes papers from professional karst hydrologists in countries like Iran, where understanding the hydrology and geology of public water sources and their near-arid karst catchments is obviously a vital matter.