[git] git: Your branch is ahead by X commits

The answers that suggest git pull or git fetch are correct.
The message is generated when git status sees a difference between .git/FETCH_HEAD and .git/refs/remotes/<repository>/<branch> (e.g. .git/refs/remotes/origin/master).

The latter file records the HEAD from the last fetch (for the repository/branch). Doing git fetch updates both files to the branch's current HEAD.
Of course if there is nothing to fetch (because the local repository is already up-to-date) then .git/FETCH_HEAD doesn't change.