The Triennial Cycle of reading Torah is when the entire Torah is divided into thirds. If a synagogue wishes to practice reading on the Triennial Cycle each week, instead of reading the full parsha (portion), only a third is read.
The general practice is to read the same third of the portion at every participating synagogue. In other words, whichever synagogue is reading Triennial will be reading the same third as every other synagogue doing the same thing each week.
For example: as of October/November of 2021, we are currently in the 3rd year of the Triennial Cycle. So any synagogue that reads the Triennial Cycle as part of their service, will be in the last third of the cycle. Next year, we begin again from the first!
Here is a useful website to check which part of the cycle we are in. The example parsha I'm using is Vayera but feel free to search for another: https://www.hebcal.com/sedrot/vayera
I hope you find this helpful!
