Additional Access is a feature that allows you to give specific contacts access to other companies, or other contact's tickets.
This setting will override the all Tickets permission, so if you want to give a contact access to all tickets for their own company and for another company, you would have to add both companies to the Additional Access List.
You can only give a contact additional access to a company or a contact, not both.
To access Additional Access Settings, all you need to do is go to your Admin Console, under Maintain Contacts, click on the name of the contact you wish to set up the feature for and scroll to the bottom.
You can see it in action in the video below: