IVR stands for Interactive Voice Response. It is a technology that allows computers and humans to interact using, traditionally, telephone dial tones and more recently by actual voice recognition. In telephony application, an IVR is a pre-recorded or dynamically generated menu system that enables identification and routing of callers. IVR systems benefit companies with the ability to service high call volumes, reduce cost and improve the customer's experience.
In practice you are probably very familiar with IVR. It is the automatic greeting you hear when calling a company that uses the technology, followed by prompt such as “Press or say 1 for sales, press or say 2 for customer service...” Your initial selection from the menu will either connect you to a relevant agent or produce a refined menu choice.
IVR is also used for outbound calls in a call center scenario where it can initiate calls to prospective customers and deliver messages and interactions that are tailored to the customer’s information. For example an IVR can deliver one set of choices based on a client’s area code and another set based on any existing CRM records.
You may hear the term Auto-Attendant used for IVR. But to be exact, Auto-Attendant is a particular application of IVR. You can read more about it in the relevant FAQ.