IVR is an acronym for: Interactive Voice Response.
Older IVR systems allowed users to call in to a system and use the keys on their telephone (also called 'touch-tones') to navigate a series of menus to get information or conduct a transaction. The system would respond to the user over the phone using Text-to-Speech.
Newer IVR systems use a speech-based interface (using Speech Recognition and Text to Speech) to permit a caller to get similar information or conduct similar transactions. The menu structure of speech-based IVRs tends to be 'flatter' than with touch-tone menus, because the available options are not longer limited to the keys on a telephone keypad.