The platform you are standing on is in waste deep water. You can kiss the dolphin, pet the dolphin, and shake it's fin while it stands in front of you. They take a picture of you kissing it, and for $30 you can purchase a video of the entire encounter. My family and I booked this directly through dolphin discovery. We all loved it.
Would do the other experience where you actually get in the water with the dolphins - - hold their fins and they pull you and you also lay on your stomach and they push you from under your feet so you are standing in the water. $129/person. There are several different experiences. All on their website -- Dolphin Discovery, Cozumel.