Hi,
Although I'm a Canon man, I'll give it a shot.
The A/M switch on the lens itself should mean Auto or Manual focus. There are times when may not wish to use autofocus of the camera. If the Nikon lenses are like most modern Canon lenses, even though you leave it on Auto, you can still override and manually adjust the focus. Can be handy at times.
And there are times when you may not want to use the VR feature such as on a tripod. Although, again if the Nikon lenses are like the Canon lenses, there may be a setting of the VR expressly for tripod use.
And I'm assuming by the selector on top, you are referring to the wheel where you choose the exposure mode. In this case, A means the camera is in fully auto mode setting both F/stop and sutter speed for you.
M mode means you don't want the camera to do anything for you, so you set both F/stop and SS, looking in the VF to get the correct exposure.
HTH
Gene