Hovering the mouse pointer over a link having a title attribute should display the title, but currently this works only when you are looking at an editing preview of the post.
There is something wrong with the translation from link markdown to HTML. The optional title field is normally translated to an HTML title attribute. The title attribute is missing when viewing a post, but is present when editing a post.
This is [an example] [id] reference-style link. [id]: http://example.com/ "Optional Title Here"
is translated to
This is <a href="http://example.com/" title="Optional Title Here">an example</a> reference-style link.
in the editor preview, but to
This is <a href="http://example.com/">an example</a> reference-style link.
EDIT: I cannot reproduce this problem on another site ([english.se]), which is why I am reporting it here and not on [meta.se].
EDIT: A post which illustrates the problem in the wild is: https://softwareengineering.stackexchange.com/a/186318/39089
EDIT: The problem was not reproducible after saving an edit to the post – even though the edit has nothing to do with the link. The problem was still not reproducible even after rolling the edit back. HOWEVER, between 2013 and 2016 the bug resurfaced. The post does exhibit the problem again, and presumably will continue to do so as long as nobody edits the post.