The Foyada Tong is the name of the independence movement on Vvardenfell, campaigning for independence from Samarkand.
When Morrowind was absorbed into Samarkand in 5E 632 there was a lot of conflict between the Dunmer, as only about a third of them wanted to join Samarkand. The remnants of the Ashlander people in particular were against this change, as it would have meant the end of their way of life forever. Not long after the incorporation into Samarkand, the Ashlanders formed the Foyada Tong to fight for their freedom.
The Foyada Tong is mostly an underground movement, with little official support. However, despite this, there are many influential Dunmer who secretly support the movement, particularly those with a lot of Ashlander ancestry. Many coups have been staged in the past, but none have been particularly successful. The group is often very hostile to outlanders, as well as to Dunmer who disagree with their beliefs, as they see them as traitors to the Dark Elf people.
At present they have made a large resurgence, and there is a definite chance that they may throw off Samarkand's yoke. This danger means that Samarkand is rather preoccupied, providing the perfect opportunity for the Empire to invade.
"Foyada Tong" can roughly be translated as "Fire-River Guild" in the Ashlander language. It was named after the large canyons sweeping though the Ashlands, which the Ashlanders saw as the perfect representation of their way of life - part of the land, but not truly of it.