Show a term description when the search filter in a view is that term?
Create a template for the view.

Edit the view. Under "Advanced" find "Theme: Information". Click on it to find the names of the templates that are applied in your theme. I think "Display output" is what you want to use. It will show you the contents of the template.

In your custom theme, create a template with the same name as the template you copied. Paste in the contents of the template you copied.

Now you can use PHP to get the information you want (available variables are listed in the comments of the templates), manipulate it as needed, and add it to the $header or wherever you want it, without any PHP in the database.