In the photo above, I have rather painstakingly unraveled the end of a 6-cord thread to show the construction.
6-cord (cordonnet) means that there are 6 plies in all: there are 3 sets of 2 plies twisted together, with all twisted yet again in the opposite direction. The result is a very smooth, durable thread with outstanding body.
Most crochet cottons commonly available in arts and craft stores are 3-cord. These are softer threads. The 6-cord is harder to find, and usually more expensive.
It's fun to experiment with different threads to see how they work up, and explore the differences in how they feel. For some projects a softer thread could be more suitable. But a beautiful, smooth, lustrous cordonnet thread is something worth trying. Because of the higher twist, the shuttle needs to be "dangled" more often to prevent the thread from kinking up.
An item made with 6-cord thread will be very hard-wearing, have sturdy picots, and be easier to block. I've never used pins when I block, ever. I just steam and shape the item with my hand.
There are many wonderful tatting shops online that stock 6-cord threads from several companies in many colors. Worth checking out. Or let the managers know at your local arts and craft store what items you wish they carried. If there is enough customer demand, they will stock more and better tatting supplies. Remember what happened when suddenly everyone wanted to knit with novelty yarns - every shop was crammed to the brim with novelty yarns!