The riddle
What Has a Mouth but Never Speaks?
Where the water ends
Wikipedia defines a river mouth as the place where a river flows into a larger body of water, such as another river, a lake, a bay, a sea or an ocean. Where the current slows, the river drops the sediment it carries, and that can build deltas, sand bars and spits. The riddle borrows the word mouth for this place.
Where fresh water meets salt
Wikipedia describes an estuary as a partially enclosed coastal body of brackish water where fresh water from rivers or streams meets and mixes with salt water from the open sea. The mix of the two is what brackish means. At an estuary the river and the sea blend over a stretch of water.
Towns named for a mouth
Many English place names say the same thing in plain letters. Wikipedia explains that Plymouth is the mouth of the Plym River, Sidmouth the mouth of the Sid and Great Yarmouth the mouth of the Yare. The same article says river mouths allow easy travel and ports, so many towns and cities were founded there. The Celtic terms Aber and Inver, for a river mouth, give names such as Aberdeen and Inverness.
Longer versions
Older books print the riddle with a second line. Dean Rivers, in 1903, asks about something with "a mouth but never speaks, and a bed but never lies in it," and Edith B. Ordway's 1915 Handbook of Conundrums words the second half as "a bed but never sleeps in it." Both answer "A river." Another riddle with a verb used in two senses is what runs but never walks.