I should add this is using 2015.1.

By design this event is fired when the widget detects change in the responsive mode. However, what your igGrid recognizes as a mode change is configurable. By default there are three modes, phone, tablet and desktop. When there is a switch between these modes responsiveModeChanged event is expected to fire.

In regards to your second question getCurrentResponsiveMode method returns the current responsive mode. If you would like to retrieve the current responsive mode in the responsiveModChanged event you could alternatively use the ui argument. For example:

//Delegate
$(document).delegate(".selector", "iggridresponsiveresponsivemodechanged", function (evt, ui) {
    //return the previous responsive mode
    ui.previousMode;
    //return the current responsive mode
    ui.mode;
});

Additionally, I made a small sample illustrating when the rsponsiveModeChanged event is fired and what getCurrentResponsiveMode method returns.

I am setting igGrid`s width option to 100%. Afterwards I am resizing the window to make it similar in size to phone or tablet. There is an alert in the event handler  showing the new mode when this event is fired.

features: [
    {
     name:"Responsive",
     responsiveModeChanged: function (evt, ui) {
                     alert("Mode retrieved using ui.mode: " + ui.mode);
     }
    }
     
    ]

Please have a look at my sample and let me know if you need any further assistance afterwards