Minecraft wiki entry for Caves_%26_Cliffs, associated text: Come in two forms, stalactites and stalagmites.
Stalactites hang from the ceiling and drip water or lava, based on what is above them. The stalactites drip water naturally without a source block above it, but these drips do not fill a cauldron.
Placing a cauldron under a stalactite slowly fills the cauldron with water or lava depending on the source block above them (enables renewable lava).
If the block on which a stalactite hangs is broken, the stalactite falls, causing damage to players and mobs directly underneath. They do not take any damage if they are airborne.
Stalagmites are found on the floor of the cave and deal damage if landed on.
The damage inflicted of pointed dripstone is directly proportional to the height from which the stalactite or player/mob falls from.