TL;DR: A unique number associated with that socket
One of the defining rules of Unix is "Everything is a file". Because of that sockets are also represented by very special filesystem, usually referred as sockfs.
Files on traditional filesystems have inode-numbers -- unique numbers that allow to identify them:
$ ls -li /bin/bash
7864369 -rwxr-xr-x 1 root root 656584 Oct 15 2014 /bin/bash
^^^^^^^
inode-number
Same applies to a sockfs, all sockets also have inode-numbers.
For special filesystems, that doesn't have actual filenaming schema, all files have generic names in form fsname:[inode-number]
(see also: linux+v3.19.1/fs/dcache.c#L2945)