A user that has the See'Queue' right can see a particular queue in RT.
This right can be granted in the global context, or on a queue-by-queue basis. Not much damage can be done by a user that has the seequeue right, but there are still reasons to limit its use; an important one is to keep the user interface clean.
Note that this right has nothing to do with tickets and in order to allow your user to see ticket you must grant ShowTicket right.
Also, note that users must relogin to see a change as RT cache list of queues a user can see.
The primary effect of the seequeue right is that all of the lists of queues that show up in the user interface of RT contain only those queues that the user has seequeue right for, The first example of this is the statistics on the home page of the user.
Because of the ubiquitous use of lists of queues in RT, the seequeue right is necessary for many basic operations on tickets.
A simple example: it will be necessary for workers on a queue (people with the OwnTicket rights) to be able to see the queue that they are working on.
A more involved example: If an organisation has a service helpdesk that uses the /service/ queue, and an applications helpdesk that uses the /applications/ queue, the workers on both of these queues will need to have seequeue rights on the other queue if they want to be able to move a misplaced ticket to the other queue.