If the Contact is already in the Admins list, you can adjust their Admin Rights by selecting Edit Admin Rights and clicking on the appropriate check box item to unlock it - or, give them the permissions for that level.
If the Contact isn't yet a Admin, you can add them and give the appropriate Admin Rights.
Storage Admin Rights
If a Contact has Storage Admin Rights, when logged in they will be able to see their Dashboard, files in the Files folder and their own Tasks.
Contacts with Storage Admin Rights will be able to upload, edit, delete, share links and view all items in the Files folder. They will be able to view any items in the Files folder created by other Admins.
Contacts with Storage Admin Rights do not have access to items stored in the Events, Meetings or Tasks folders (or, if your Organisation uses the add-on, Pages).