The characters combine to create a powerful visual metaphor: “Mouth [is] like a hanging river.” A “hanging river” (悬河) is a classical Chinese image for a waterfall, a river that seems to be suspended in the air before it crashes down. The idiom therefore paints a picture of words pouring out of a person's mouth with the same unstoppable, magnificent force as a waterfall.
口若悬河 is a literary idiom (chengyu) but is still widely understood and used in modern conversation, writing, and media. Its connotation can shift from positive to slightly negative based on tone and context.