This is a short string (i.e., sequence of characters) that is added to
the end of the base name (i.e., the main part of the name) of a file
or directory in order to indicate the type of file or directory.
On Unix-like operating systems every directory contains, as a minimum,
an object represented by a single dot and another represented by two
successive dots. The former refers to the directory itself and the
latter refers to its parent directory (i.e., the directory that
contains it). These items are automatically created in every
directory, as can be seen by using the ls command with its -a option
(which instructs it to show all of its contents, including hidden
items).
They are special name-inode maps which do count as hard-links (they do increase the link-count) though they aren't really hard-links, since, as you said, directories can't have hard-links. Read more here: Hard links and Unix file system nodes (inodes)