When hovering over a tag 'under' a question, a popup with extended information is shown. While the usefulness is under discussion, and people like me write userscripts to fill the gaps, I noticed it's not being applied consistently throughout the system.
In posts, you can use Markdown commands
[meta-tag:] to show nicely formatted tag links like discussion. They look exactly like the tags under the question, yet when you hover over them you only get a meager link description (left):
This leads to situations where the tag in the top of the page has a hover popup (right), but the same tag a few lines below doesn't.
Curiously, while writing this post, I noticed that the preview does have a hover for the tag (left):
Another place to add the popup would be the 'Related Tags' widget in the right sidebar of the tag info pages (right).