This add-on allows you to designate one of your EE categories as the primary one for that entry (per category group). Primary Category takes over the Categories field in the Publish page and extends the functionality. You select your categories for the entry as usual, but then with 1 extra click you can then select which of those is the primary/main category for that entry. There's a wide range of reasons why you might want/need to do this. On the front end in your templates, special variables for that category become available.
Additionally, you can also have Primary Category remember the categories and primary categories you assign to an entry and then to apply those to the next entry, as well as configure the extension to require a Primary Category be selected on a per channel basis.