Oxygen is an in-game mechanic related to Moistness and having to do with water. Oxygen is an indicator of how long a dinosaur can survive underwater before they begin to take damage.
Terrestrial Dinosaurs/Aerial Dinosaurs
The majority of Aquatic dinosaurs have infinite oxygen. Their natural element is water, so they instead have a moistness gauge for when they're out of the water. A few exceptions to this rule are Mosasaurus and Pliosaurus. They have both oxygen and moistness, potentially as a balance for their powerful combat statistics. Their oxygen is much greater than 10, however. Mosasaurus' oxygen is 600, meaning it only needs to go the surface every so often for air.
Hybrid refers to dinosaurs that live both on land and in water. These dinosaurs include Spinosaurus, Baryonyx, Sarcosuchus, and Megavore. These dinosaurs are able to breathe and swim underwater normally, while surviving primarily on land.