WebDAV is an HTTP-based network protocol used for mounting remote files as a local drive. We use it to mount local (encrypted) files as a drive. It is the drive you see in your Windows Explorer (or whatever operating system you use), when you unlock your vault.
Despite the fact we just use it to connect from your local machine to your local machine, it is still a network protocol and thus needs a port. The socket, however, is only listening to loopback connections and the drive is not accessible from other machines in your network.
Edit: Oh yet another thing: You can copy the WebDAV URL and use it from 3rd party softwares (given that they run on the same local machine) to access your vault, too.