Snowflake formation starts in a cloud composed of water droplets adhering to small particles of dust and dirt. This water evaporates and forms vapor within the cloud. In a process known as deposition, the water vapor turns directly into solid ice at very low temperatures. The microscopic ice crystals grow until they are heavy enough to begin falling—as snowflakes.
The traditional picture we have of snowflakes is one of a single ice crystal with six identical arms, but these perfect specimens are generally in the minority in nature. Snowflakes range in shape from hexagonal plates to long thin needles, to squat hexagonal columns, and even hollow columns. In addition, a large number of irregular snowflakes do not have a specific shape and even lack the almost universal hexagonal symmetry. The shape of the flake is determined predominantly by the temperature and humidity when the vapor turns into ice. At lower humidity, the platy and columnar shapes dominate; with higher humidity, the more complex six-armed beasts tend to dominate. For a fixed humidity, the shape alternates from platy to columnar to platy to columnar as the temperature falls from 0°C to -30°C. Why these shape transitions occur for small changes in temperature is not well understood.
So why is each snowflake different? As they fall, snowflakes are subjected to a myriad of microclimates with large variations in temperature and humidity. The final shape of a snowflake moments before it lands on your nose is determined by all the different microclimates through which it has passed. Because the paths are unpredictable and highly variable, no two snowflakes pass through the same set of microclimates and as a result each snowflake is unpredictably unique.