You can adjust category's name and section on this page. You can optionally specify "description" for the category (HTML allowed) that will be shown on the "new ticket" page and in the Knowledge-base
Adding a pre-filled ticket template for the category allows setting default subject/body on the "new ticket" page (after the category has been selected).
You can also edit users permissions for this category, by adding them to the list of technicians.
Technician - is a user who is permitted (by an administrator) to handle tickets in one or more categories. A technician receives email notifications about every new ticket in a category. To make a user a technician - simply add him to the list.
By default, everyone can create a ticket in a category, this is the recommended option to prevent things from becoming too complicated. But you can optionally grant ticket-creation permissions as well - to specific users and companies.