"Chatter" are the vibrations you feel through your board as you ride. They become more prevalent the faster you go, and are a sign of the stability and dampening of your board. Can happen in a lot of conditions, but obviously the harder the surface, the worse the chatter can be.
When your board chatters it is because of the pressure of the riders weight down on the board, body alignment above the board, body movements with the board not being able to actively absorb/manage the interaction of pressure between them, their board and the snow. When your board is chattering it is NOT at indication of stability but rather a sign of instability of the edge of the board leaving the snow. Most people will experience "chatter" on harder snow conditions.