Show term description when grouping by taxonomy term
One option for solving this is to rewrite the output of your view fields to meet your formatting requirements, which consists solely of configuration steps -- no code changes needed :).


On your view, add the Taxonomy: Term field and the Taxonomy: Term description field.  Make sure the Term field is above the Term description field.
Next, edit the Term field, select Exclude from display, and click Update.
Now, edit the Term description field and check Rewrite the output of this field. You can set this Term description field to include the formatting you desire of your Term name and Term description using the available tokens, which are listed in the Replacement patterns fieldset.


For example, try placing the following into the rewrite Text textarea:

&lt;h1&gt;[name]&lt;/h1&gt;
&lt;p&gt;[description]&lt;/p&gt;


Be sure to click Update after you have finished configuring the Term description field.


Last, in your field settings, select Group by Term description and voilà, you should have all the data you want in each grouping section. As long as your term names or term descriptions are unique, this should group as expected.