There are four basic shapes of ice crystals: the hexagonal plate, the needle, the column and the dendrite. The dendrites are hexagonal with elongated branches, or fingers, of ice; they most closely resemble what we think of as snowflakes. The temperature at which the crystal grows determines the particular shape. A snowflake is an individual ice crystal or an aggregate of ice crystals. Large snowflakes are aggregates of ice crystals.
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 dendrites collide, it is likely that their branches will become entangled and the two crystals will stick together. When two plates collide there is a good chance that they will simply bounce off one another.
Temperature also plays a role in aggregation. If the temperature of one crystal is slightly above freezing, it may be encased in a thin film of liquid water. If this particle collides with another crystal, the thin film of water may freeze at the point of contact and bond the two particles into one. (Similar physics underlies why you should never lick a cold metal flag pole.)
Snowflakes composed of aggregates can sometimes reach 3 or 4 inches in size. The record-size snowflake occurred in January 1887 in Fort Keough, Mont., when some flakes were measured at 15 inches in diameter. That is about the size of a family-sized pizza pie.