Modern business phone systems provide a number of features that help manage customer contact via the phone. An auto-attendant is a key feature of Hosted PBX/VoIP phone systems that enables you to direct phone calls without the need for human intervention to:
You've probably already used an auto-attendant (aka IVR) when you've ended up in a call centre - it's the Press 1 for this, Press 2 for that.
Depending on the customer's selection, you can then instruct the business phone system to take the required action which can be to play a recorded message, transfer to a person or group etc.