Grinding typically takes place in a large drum. As material is fed into the rotating drum, plates or grooves in the side of the drum lift the material up along the side. Once it reaches a certain height. the grooves or plates can no longer hold the material due to gravity and it falls. When the material falls it hits the side of the mill or ideally lands on more material and breaks - by impact forces. In addition to impact forces, material is also ground by attrition (friction) forces, as particles move past each other or some grinding media.
Figure: Autogenous (top) vs. semi-autogenous (bottom) grinding.