The propylon chamber system was devised to allow instantaneous travel among ten ancient Dunmer strongholds, which are scattered across Vvardenfell and quite isolated. Each chamber links to two others, forming the propylon circle.
To transport to a specific stronghold, you must be carrying the correct propylon index. The indices are scattered across Vvardenfell, and often go unnoticed because they are so small. Chances are not very good that you will stumble across all ten on your own, but fortunately there is a list of index locations.
The need to carry all ten indices and to follow the propylon circle in order is eliminated by the Master Propylon Index. The master index is a direct link between Caldera and every propylon chamber. It was not part of the game originally, but Bethesda added it with an official plug-in which can be downloaded here. The plug-in has Folms Mirel send you on a quest to retrieve every index, being given the master index as a reward.
Propylon Chambers are found in these Dunmer strongholds:
There is also an eleventh Propylon Chamber located in Kogoruhn, though it is now no longer functional.