When you push to a remote and you use the --set-upstream flag git sets the branch you are pushing to as the remote tracking branch of the branch you are pushing.
Adding a remote tracking branch means that git then knows what you want to do when you git fetch, git pull or git push in future. It assumes that you want to keep the local branch and the remote branch it is tracking in sync and does the appropriate thing to achieve this.
You could achieve the same thing with git branch --set-upstream-to or git checkout --track. See the git help pages on tracking branches for more information.