A queue is simply a workflow process notification system. A user within a role can promote into or out of a queue based on the queue permissions set in configuration. Queues are triggered when a user wants to notify either another user in same role, someone in different role, or even a third party that a record is ready for action or needs review.
Your role allows you to see queues to know where a record is sitting and the next process awaiting action. Also, it is a historical reference of who put it in each queue in the event a question arises during your process action. Queues have the ability to set a structured business flow so let's say a booking goes through the same steps each time. It is very important all roles review their queues so workflow happens in a timely manner. If a record is queued to your role you will see it in your list, take whatever action the queue expects, and when you've completed your part, you would then click "promote to next" to move the transaction along to next task.
Note: not all queues trigger another queue; some may go to "none" depending on what configuration has been set. Do not uncheck a queue when complete as this stops the expected workflow and may cause unknown errors to occur within the process flow. Always use the "promote" function as this provides a historical list in the event we need to recreate a transaction. The check box is used to place a record in the queue to get started. Now you may unchecked the box, but only if you inadvertently placed it in before ready (but note the next user may have started acting on it) or if you need to send back to originator to take action at which time they would start the flow over by promoting in.
See also Queues.