Current browsers will display a tooltip for anything in the “title” attribute in HTML.
Here is the HTML for an image I inserted into my test blog just now:
<img class="aligncenter size-full wp-image-7112" src="http://design5279.files.wordpress.com/2014/03/img_6030.jpg" alt="IMG_6030" width="523" height="392" />
To see the HTML, open a post for editing and click on the Text tab at the top right of the editor area.
http://en.support.wordpress.com/editors/#text-editor
If I add this somewhere inside the angle brackets and save:
title="Looks delicious!"
Then I can see the tooltip when I hover over that image. Here’s what the final HTML for my test image looks like:
<img title="Looks delicious!" class="aligncenter size-full wp-image-7112" src="http://design5279.files.wordpress.com/2014/03/img_6030.jpg" alt="IMG_6030" width="523" height="392" />