Pillars are a stalactite and a stalagmite grown together. Alternative terms are column or stalagnate.
Stalactites form, where calcite rich water enters the cave at the ceiling. The water looses carbon dioxide (CO2) to the cave air and is not able to hold all the dissolved limestone any more, and a certain amount precipitates. When the drop grows and falls down, it will again loose some carbon dioxide because the drop splatters and becomes an enormous surface which makes the exchance between water and air easier. Again the water is not able to hold all the dissolved limestone any more, and a certain amount precipitates on the floor and forms a stalagmite. So it is very common, that stalactites and stalagmites grown at the same time and same place. They grow towards each other.
If they grow big enough, stalactites and stalagmites meet and join. But as they grow very slowly it takes hundreds of thousands of years. After they met they are called a pillar or column. Sometimes the scientific term stalagnate is used, but it is not common any more. Pillars are not really a different speleothem, but they are the late stage of stalactites and stalagmites.
Once the pillar has formed the water does not drip any more, so the growth of the pillar differs from the growth of separated stalactite and stalagmite. Now the water which runs down on the outside, without dripping. After some time the pillar looses the typical shape with a thick lower part and a thin upper part, and becomes a more or less cylindrical column. The former stalagmite and stalactite are not easily identifiable any more.
There are numerous shapes of such pillars, as there are numerous shapes of stalactites and stalagmites. Most common are the ones looking like on the image to the right: Upper end thin, lower end thick and a little bit like a pyramid, getting thinner step by step.
It is rare but possible, that stalactite and stalagmite are not formed at the same time. This is e.g. when the floor is covered by a cave river in river caves. The water flowing on the floor makes the growth of a stalagmite impossible. But if the stalagmite becomes long enough to reach the floor it will still form a pillar. Obviously it needs a dry period to finally reach the floor, but water levels and flow rates in caves change continually.