Though the main flow of the Everglades is in an area called Shark Valley, you won't find any sharks here. Nevertheless, it is indeed a valley. The 'mountains' on either side of the valley are only a few feet high, but that is just enough to keep the water contained as it flows southward from Lake Okeechobee. Flowing water through a valley is called a river anywhere else, and it really is no different here. Despite what most people think, the Everglades is not a swamp. A swamp is a wetland with trees growing in the water, and has very little flow.
The Everglades is truly a river -- a very wide (up to 40 miles), shallow (usually no more than a foot or so), very slow moving river. The headwaters are actually up near Orlando, where the water flows through the Kissimmee River to Lake Okeechobee. Historically, the lake would overflow its southern rim during the summer rainy season. The water then flowed through the valley, slowly turning to the southwest as it joined up with the Shark River (Oh! Now I get it!). Nowadays, the lake has a big dike around it, and the waterflow is largely controlled by floodgates and canals. In Everglades National Park, though, the water flows very much the way it always has.
By the way, in case you are wondering why the Shark River is so named, it is because sharks supposedly come into the mouth of the river to give birth.