A snowflake can be an individual ice crystal or an aggregate of ice crystals. Ice crystals can grow by water vapor deposition on the crystal or by collisions with other cloud particles.
An ice crystal can grow if the air around it has a relative humidity near 100 percent. The ice particle grows by water vapor deposition. Growth by deposition is generally slow. If you find nicely shaped snowflakes, they likely were produced by vapor deposition.
Collisions can produce large snowflakes. When an ice crystal falls through a cloud it may collide with and collect super-cooled liquid water drops. This process of ice crystal growth by sweeping up water drops is called accretion. When ice crystals collide with super-cooled drops, the drops freeze almost instantly, providing a mechanism for the particle to grow quickly.
An ice particle produced by the accretion process that has a size between 0.04 to 0.2 inches and no discernible crystal shape, or habit, is called graupel. On collision and freezing, the super-cooled water often traps air bubbles. Because of this trapped air, the density of a graupel is low and it can easily be crushed, unlike a hailstone.
Aggregation is the process by which ice crystals collide and form a single larger ice particle. The probability that two crystals will stick together depends on the shape of the crystals. If two crystals with spiky appendices collide, it is likely that their branches will become entangled and the two crystals will stick together. Snowflakes composed of aggregates can sometimes reach 3 or 4 inches in size.