It's extremely useful especially when, for any reason, the device goes offline or it's being put under an extraordinary stress, like for instance when you send many messages at the same time.
In these scenarios, messages that cannot be delivered right away will be stored in the queue so that when the device is back online and synced, they will gradually get sent according to the priority that you had previously established: "urgent" and "high" priority messages will be sent within a few minutes, whereas "normal" and "low" priority could take some more time.
Depending on how long the device has been non-operative or out of sync, the queue could take more or less time to decrease, however, please allow it up to 10 minutes before panicking.
Please note that messages that are scheduled for a later delivery will also be stored in the queue and will be sent when they are scheduled to be sent if the device is online and operative.