If the caller does not select an option once they are through to your IVR, the menu will automatically be replayed after 10 seconds (unless you have specified something else).
In total the menu will be played 3 times and after this if the caller still does not press any options, the call will be disconnected, but the menu can be defined such that option 0 points them through to the same menu.
It is also possible to have the default option set so that if the caller does not select anything then it dials a specified number.
In this instance your recorded greeting would have 'press 1 for x department, press 2 for x department' options as well as something like 'or please hold to speak to an operator'. This is useful if your caller does not have DTMF.