Premise: the queue is a tool that allows you to momentarily store all the messages that cannot be dispatched immediately when you send them, together with the ones that you schedule for a later time.
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.