The Reach was subdued by the empire beginning with Tiber Septim (see for instance, the quest at the Old Hroldan Inn). The Forsworn are those who seek to rid the region of both the empire and the Nords, and have turned to daedric magic in a pact with the hagravens in order to "repay every debt in blood" (see
The Legend of Red Eagle).
During the Great War, the empire pulled its troops out of the Reach in order to secure the Imperial City. During this time the Forsworn took the city of Markarth and ruled it for 2 years. After the Great War, Jarl Igmund's family contracted with a Nord militia led by Ulfric to retake the city from the Forsworn. In exchange they said they would allow Talos worship in the city. Igmund says they hoped the Thalmor would not find out about it. The city was retaken, but the Thalmor did find out about it, so to prevent a renewal of the war with the Dominion, Igmund's father had Ulfric and his men jailed. This whole deal is called the Markarth Incident.
Spoiler In their dossier about Ulfric, the Thalmor claim that they engineered the whole thing.
There are some in-game books about the Forsworn. The latter two are written by the same guy, and let's just say he's very opinionated and has quite a rosy view of the Forsworn. IMO he is not an objective source, so you have to read between his lines very carefully. Some of the information in
The Bear of Markarth is contradicted by Igmund and others, for instance.
http://www.uesp.net/wiki/Skyrim:The_Legend_of_Red_Eagle
http://www.uesp.net/wiki/Skyrim:The_%22Madmen%22_of_the_Reach
http://www.uesp.net/wiki/Skyrim:The_Bear_of_Markarth