Originally we planned to do a couple of cavern dives and do more diving or snorkeling in the sea, but most of the time it was too windy to launch the boats and we ended up only doing cenote dives.
The Yucatan Peninsula is a completely flat limestone shelf. Years ago when the water level was lower cave systems were formed by rainwater percolating through the porous rock. Later, when water levels rose again, these cave systems were flooded. Today all the rivers in the Yucatan run through these underground systems. There is more information about the caves of the Yucatan at Quintana Roo Speleological Survey.
I've done some potholing in the past in the Mendips (UK), and it was always disappointing to see the damage to stalagmites and stalactites that had occurred - when they're in situ they look good, when you break them off they're just a lump of rock.
Because less people get into the cenotes, and also because the guides are very conservation minded, the formations we saw were generally in very good condition.
Cavern/Cave diving is more difficult than open water diving and has some different risks. You need extensive training to do Cave dives. Cavern dives can be done without extra training, but there are some additional safety procedures you have to follow.
In some ways Cavern dives are easier than diving in the sea - usually they are shallower, and you don't have to worry about currents or being distracted by fish or coral. But usually you can't directly ascend to the surface, it's dark and disturbed sediment can reduce visibility quickly. It's also easy to get disorientated.
We dived with the Cenote Dive Centre in Tulum. On every dive they explained the safety procedures and we felt very safe with them. Twice when I went there were divers who were very nervous before the dive. Both times (with different guides) the guide reassured them, sorted out any problems (before and during the dive), and at the end both were delighted that they'd done the dive.
We started with a refresher in Casa Cenote which contains a mix of fresh and salt water. This was not a cavern dive, but was interesting because it's surrounded by mangroves.
The next day we dived at Dos Ojos and The Batcave - two dives starting from the same site. Dos Ojos was very nice - very clear water and amazing formations. The Batcave was even better.
The next time I went to Calavera (the Temple of Doom) and Gran Cenote. In Calavera the water was noticeably green, and the entry was a giant stride from a height of 2-3 meters. This Cenote has a Halocline, where freshwater lies over saltwater. Where they mix you get interesting visual effects, which can be quite disorientating.
Gran Cenote was similar to Dos Ojos - again very clear water and nice formations.
On the last day the weather was still too windy for sea diving, so I had a choice of repeating Dos Ojos/The Batcave or not diving. It was an easy choice; the Batcave was my favourite so I was happy to do it again. This time we got there a bit later, there were more divers and so the visibility was worse, but it was still a fantastic dive.