This may be more information than you wanted, but:
The Yucatan peninsula is a big limestone plateau. There are no surface rivers; all the water that falls as rain, runs to the sea underground. This water has dissolved the limestone, creating passageways. From time to time, the surface falls in over one of these underground rivers, creating a sinkhole, or "cenote".
Some of the cenotes are good sized, and are used for recreational swimming and snorkeling. Many of them are dived. For open water divers, tours in the cavern zone are offered. The cavern zone is defined slightly differently by different dive agencies, but the essence is that it is the zone where you are beneath a stone overhead, but still able to see ambient light somewhere. The cavern tours are supposed to be led by a guide who is at least an OW instructor AND full cave certified, and is diving full cave gear (doubles, long hose). The dives follow the permanent guideline, or where there is none, a line is to be run. All divers have lights.
The cenotes dives, for people who have enough experience to be confident in the water, and who have good buoyancy skills and the ability to maintain a more or less horizontal position in the water, are a fantastic way to get a small introduction into diving in overhead environments, and why one might want to go on and get cave trained.
Here is my writeup of my cenote tours from our Cozumel trip in March of '07.