Icicles form on sunny days when the ambient temperature is below freezing. Heat from the sun melts ice or snow on surfaces to form water drips. A few drops refreeze to begin the base of the icicle, and as water continues to drop, the icicle grows in length.
For the water that drips from the roof to refreeze, it must dissipate heat into the atmosphere. The air surrounding the icicle forms an insulating buffer. This buffer is thicker at the top of the icicle, so the water moves toward the bottom of the structure, where there is less insulation, before it refreezes. This movement of water forms the thin sheet of ice that causes icicles to grow longer and thinner at the bottom.
As the ice crystals build up on the icicle, they take the shape of an inverted cup. Most of the time, this cup fills instantly with more cold water ready to form additional crystals. However, occasionally the cup fills with air; as more ice crystals form over the trapped air, it gives the icicle the characteristic cloudy look.
Once the sun is no longer shining on the snow to create water flow required for active growth, the icicle continues to change shape. At subfreezing temperatures, some of the ice transforms directly to water vapor in the atmosphere. The process smoothens the outside of the icicle.