From AMS Glossary
Ice in the shape of a narrow cone, hanging point downward from a roof, fence, cliffside, etc.
An icicle is formed when above-freezing water, for example, snowmelt or groundwater, runs or drips into subfreezing air. The water freezes as it drips or runs, forming a narrow cone pointed downward and growing in both length and width, widest at its top. Most icicles are found hanging from the edges of heated, snow-topped roofs, with any water that has not frozen in its downward traverse forming ice on the surfaces below.