A user who belongs to the owning organisation but is not set up as an Agent will be treated as a Staff user. A Staff user can view tickets belonging to others in the organisation (if the Role they have allows this). They will not be able to answer tickets coming in from customers or from other staff users. See more on Managing Roles.
A staff dashboard will have three default queues visible and a list of statistics across the top as usual giving a quick view of number of total tickets, unassigned tickets, waiting for an agent, waiting for customer and resolved.
The three queues are Created by You, Assiged to You & Watching.