From Tolkien Gateway
The Redwater was a river that ran near the eastern fringes of the known part of Middle-earth. It rose among the Iron Hills, east of Erebor, and from there it flowed southwards until it met the River Running in the middle of that river's course. Its name is direct translation of the Elvish Carnen, and seems to be a literal description: rivers that flow out of land with strong iron deposits do indeed show a distinctive red-orange colour in their water.
Little is known of the peoples who lived along the river, except for the Northmen who lived in the lands west of the Redwater in the Third Age. These Men enjoyed a strong alliance with the Dwarves of the Iron Hills, maintaining a prosperous community in this region.