Data watchers are used when you need to send server information to the client or client info to the server. In most cases, this is going to be a variable determined server-side that you want to use for rendering.
In your example with the wolf, the health is only calculated on the server side, but the wolf's tail needs to render at an angle based on its health.
In some cases, the variable will be calculated the same on both the client and server sides or the variable is only needed on the side it is calculated by, so data watcher is not needed.