The River Isen (or Angren in Sindarin) began in the southern Misty Mountains, first flowing south through the fortress of Isengard (or Angrenost) to the White Mountains, where it abrubtly bent west and flowed to the sea of Belegaer.
The Isen and Adorn formed the boundary of the Kingdom of Rohan, but the triangle of land between Isen, Adorn, and the White Mountains was a contested land, claimed by the Rohirrim as well as the Dunlendings.
The Isen formed a natural boundary in the Gap of Rohan, and was only crossable at Isengard or at the Fords of Isen, where the Rohirrim fought a number of great battles against the Dunlendings and Saruman's Orcs in the late Third Age.
Saruman diverted the Isen away from Isengard as he turned the fortress into a war machine, and it was dammed at the northern wall. When the Ents attacked Isengard, they broke the dam and restored the original flow of the river, temporarily drowning all of Isengard.