The Yazoo begins in Greenwood, Mississippi at the junction of the Tallahatchie and Yalobustia rivers. Now Greenwood is already in that part of the Mississippi River floodplain called the "delta"; you'd think that the river would flow directly west into the Mississippi River.

But no, because the Mississippi has built up a series of natural levees1, the Yazoo flows south for 100 miles or so (through Yazoo City, of course) until it empties into the Mississippi near Vicksburg, probably following an old course of the Mississippi2.

As it turns out, a small river flowing in a larger river's floodplain, running parallel to the larger river, is a fairly common occurrence. The Delta region alone has several dozen of them. The Yazoo River has given its name to this type of landform. The Tallahatchie River, one of the Yazoo's principal tributaries, is a yazoo. In fact, most large river floodplains will have at least one yazoo.
1You can't possibly have thought that Humans thought that up on their own.
2I have also heard of a theory that during the last Ice Age, the Ohio River didn't empty directly into the Mississippi; instead, they flowed parallel to each other through the Delta, only merging near Vicksburg.