means The opening in the face used for eating, speaking, and breathing — and, by extension, any opening shaped like one, such as the mouth of a river or cave.

from From Old English 'muth,' a solidly Germanic word with cousins all over the family tree — Dutch 'mond,' German 'Mund,' even a likely deep relation to Latin 'mentum' (chin). The river-mouth and cave-mouth senses are old too: speakers have long seen a gaping opening and reached for the most familiar gaping thing they owned, the one on their own face.