WordPress does not give you the option to create an introduction or at least a description like it does for categories.
unBlock gives you the ability to create a custom blog home introduction (Premium version only).

We do this a little differently from other themes that offer this capability by selecting a page for your intro. There may be times when you want a little more than just 1 line for the title and 1 for the intro, so a page works best.

- Go to Appearance > Customize > Blog Options
- Look for the Page with a Blog Welcome Intro setting and select the page from the dropdown list. Make sure you have a page created before doing this.
- Click the Publish button.