Call Queueing is putting your customers to wait (in a virtual call queue) when all your agents are busy. This is optional, that is, you don't have to ask your customers to wait (in the queue). You could also do other things like "Say Sorry and Hangup" or just cut the call & send an SMS saying "Sorry, all of us are busy now. We will call you back".
It looks like this in the Connect applet:
Lets say you were connecting to the "Sales" group in this connect applet, and if everyone in the sales group is talking to someone else ("busy" state), then the next caller will be put on the queue. In the above example, before getting into the queue, he will hear "Please hold for sometime. All our executives are busy". Once he is in the queue, he hears a certain music for a maximum time of 3 minutes.
In this three minutes, if any of the agents in the "Sales" group finish their conversation, then the caller is automatically unqueued and connected to that agent. The order is "First in first out".
Please note that if there are no agents in the "Sales" group of if their agent's device status is "off" or if their phones are unreachable etc, exotel will not put the caller in queue as it is likely that the caller will never have an agent to talk to. There has to be an active ON agent in the group and the agent has to be talking to someone through the exotel system (either through incoming or outbound call).