These are natural caverns, carved by water in the soft limestone which is the main rock type in that part of Mesoamerica. I've been inside huge caves in the Maya Mountains of Belize and have read recent accounts of caverns that extend for many miles. Archaeologists are finding many items of great interest in these caves.
The big Cenote at Chichen Itza is typical of the many sinkholes that underlie this region. SCUBA-equipped archeologists are finding large numbers of important artifacts because the Maya (and probably their predecessors) believed they originated in this underground realm. Many sacrifices (including human ones) were thrown into the cenotes to placate various gods.
Thanks! I am familar with limestone caves. Discoveries like these are one of the reasons why I loved having a National Geographic subscription as a kid.