Depoists of calcite precipitated from solution in the ground-water feeding them. The calcite (crystalline calcium carbonate) has been dissolved from the limestone around the inlet.
Stalactites hang from the ceiling of limestone caves, while stalagmites rise from the floor. Stalactites form as mineral-rich water drips from the cave ceiling, leaving behind deposits of minerals that accumulate over time. Stalagmites form as the drips fall to the floor and build up mineral deposits in a cone shape.
They develop strange, twisty shapes, grow horizontally, branch or otherwise behave weirdly. No-one is really sure how, and of various theories, some may apply to some helictites but not others! I have seen one form, in one cave and one only as they are all unique, resembling something from a Mediaeval church. They were only about 20mm high, each consisting of a thin straight stem with a little cross-arm. The three tips each held a tiny, exquisite "botryoid" (a cauliflower-like formation) no more than 3mm across. Unfortunately none of us in out team photographed them. I have also observed "outdoor" helictites - actually inside a building. These tiny examples are growing outwards from a ball-valve maintaining the level in a laboratory tank, and resemble little, pure-white whiskers up to 3mm long.