“Prune remote branches” in Git Extensions executes git remote prune command, which removes your local remote tracking branches where the branch no longer exists on the remote.
See here: https://git-scm.com/docs/git-remote#Documentation/git-remote.txt-empruneem
This just garbage collects your branches.
Thats means, if an object (a commit) cannot be reached in any of your branch’s ancestors, it will be removed for the git database, and as such couldn’t be reach anymore.
This just cleans up a little the git repository and make it lighter.