Rob from Twilio here. Very fair question - a lot of these concepts are foreign for folks that haven't worked in the call center space before.

I think Al Cook on our product marketing team described it most aptly as referring to Task Router as "ripping the still-beating heart out of a high volume call center and sitting it on a table for a developer to plug in his/her app."

Task Router is a set of primitives that takes the state that must be managed to accept work from multiple channels and delivering it to resources that can complete them. You can define the core logic to accept tasks from any channel, assign it to the appropriate workflow based on its attributes, and connect it to a resource ready and able to complete it. These flows are defined by you, all without re-implementing the state management common to this problem domain.

Does that help?