(N/A) The $p-T$ phase diagram of water shows that the fusion curve (the boundary between solid and liquid phases) has a negative slope. This means that for water,an increase in pressure at a constant temperature near $0^{\circ}C$ lowers the melting point of ice.
When crushed ice or snow is squeezed in the palm,the pressure applied at the contact points between the ice particles increases. Due to the negative slope of the fusion curve,this increased pressure causes the ice to melt locally,even if the temperature is slightly below $0^{\circ}C$.
As the pressure is released (when the hand is opened or the pressure is redistributed),the local pressure drops back to atmospheric pressure. Consequently,the water that was formed by melting refreezes,acting as a binder that fuses the individual ice particles together into a solid,stable ball.