Stalactites are dripstones pointing vertically downwards from the cave ceiling.
Stalactites are deposited by driping water. The drop is formed at the ceiling by water coming down a crack, hold against gravity by the surface tension of the water. When the water drop grows, there is a point where the weight of the water gets to large for the surface tension and the drop falls down.
But in the time between two drops, some amount of carbon dioxide (CO2) goes from the water into the caves air. Without this CO2 the water is not able to keep all its limestone, and a tiny amount of limestone precipitates at the ceiling. It first forms a ring around the drop, then a soda straw.
Normally after some time a little dirt or calcite fills the soda straw and forces the water to flow on its outside. This is the moment when the soda straw becomes a stalactite.
The diameter and shape of the stalactite depends on the amount of deposited limestone and the amount of water. If there is very little water, it will flow rather slow and most of the limestone is deposited near the ceiling. This results in thick stalactites. If there is much water, the limestone deposition takes place all over the stalactite and it will be rather thin and long.
Stalactites are always thinner than other drip stones, especially stalagmites, and have a pointy lower end.