Megasaur has the perfect answer to your question about what it means to "condition the body". My answer below is meant to be supplementary.
Regarding your question on the application of treading water, I can answer that since my water polo practices in high school required treading water as an exercise in itself. Have you ever tried to tread water for 5-10 minutes without stopping? It can tire the legs very fast. It has a similar effect as doing leg squats. Your legs will feel numb after several minutes if you're not used to it.
Because of this, treading water is often accompanied by sculling water with the arms to make it easier on the legs; this works as a full body workout (the application in this context of treading water). That's what those divers likely do at the ocean surface level while chatting with their friends. Treading can be done in other ways too. My high school water polo practices had everyone tread water with arms raised above water for several minutes, to maximize conditioning benefits. Even if arms are kept down and not used to scull water, it is still a great workout for the entire body. Your upper body gets respiratory benefits, plus the upper chest muscles and abs muscles are used too.
Kick-wise, treading water can be done using a flutter kick or by kicking like a frog one leg after another. Divers regularly use flutter kick to navigate through the depths... so treading water using flutter kick shouldn't be hard for them, although most people probably find the frog version of the tread kick easier. However, each type of kick also targets different leg muscles for conditioning so both can be alternated if one type of kick wears out your legs. As indicated by the article, treading water is great for conditioning the entire body.