You are right - remote branches really reflect the branches in the remote repository.
Branching of the remote branch and remote tracking is used to indicate the branch of the form refs/remotes/<remote-name>/<branch-name> , which is reported, for example. like origin/master . (Note that this is sometimes confused with the concept of a branch that tracks the remote branch, for example, your main branch is connected to the source / master. The terminology is unsuccessful, but we are there.)
The purpose of the remote tracking branch is to remember the last known position of the branch in the remote repository. This is necessary for git pull work; it is retrieved from the remote branch (the main source branch), stores this in the remote tracking branches ( origin/master ), and then merges it locally. Records can only be created locally, and merges can only be performed in the work tree, so this is absolutely necessary!
The remote tracking branch is also useful, as you say, to learn what is happening in the remote repository. By default, all remote branches have remote branches, so you can easily use git remote update [--prune] <remote> or git fetch <remote> to update them, and then check them out and play with them as you see fit. Please note that you can do something other than checking - you can distinguish between them ( git diff origin/master ), find out what makes you happen, what you don't ( git log master..origin/master ), or anything whatever you like. Since all history exams are local, the remote branch should be there for you.
Since git push affects branches on the remote control, it naturally updates the remote tracking branches; it would not be wise to change the boss-master, and then pretend that he is still in the same position until you bring! But in fact, it does not depend on the branches of remote tracking. (If you set push.default to tracking, it will use your tracking configuration, such as master master origin, to determine what to click on. But it still is virtually independent of the remote tracking branch.)