The video tracks formation of snowflakes from their origins in bits of dust in clouds that become droplets of water falling to Earth. When the droplets cool, six crystal faces form because water molecules bond in hexagonal networks when they freeze. It explains that ice crystals grow fastest at the corners between the faces, fostering development of the six branches that exist in most snowflakes. As snowflakes continue to develop, the branches can spread, grow long and pointy, or branch off into new arms. As each snowflake rises and falls through warmer and cooler air, it thus develops its own distinctive shape.
Produced by the American Chemical Society.
Edit: And here’s a bonus video listing various interesting facts about snow: