Why do dendrites form in metal alloys?

Dendrites are the snowflake-like shapes in metal microstructures. These are different in nature and origin than lamellar structures from eutectic or eutectoid reactions. These come about because of instabilities along solid-liquid interfaces. If your solid material absorbs a large heat of solidification then the liquid can be at a lower temperature than the interface and therefore a protuberance sticking out into the liquid has a driving force to persist and grow. Then protuberances can grow off the side giving rise to the characteristic dendritic microstructure.