the mouth: the opening in the face through which a person or animal eats, drinks, and breathes
This is the plain, physical meaning. The mouth is the part of the body food and drink go into and the part an animal can bite with. The New Testament uses it for an ordinary human mouth (the coin in the fish's mouth, vinegar lifted to Jesus' lips), for fierce animal mouths shut or escaped (the lions Daniel faced, the bit set in a horse's mouth), and for the terrifying mouths of the visionary creatures in Revelation, out of which pour fire, smoke, water, or foul spirits.
Because the mouth is an opening, the same word stretches naturally to the picture of the earth opening its "mouth" to swallow the flood the dragon spews. That is the one place the word names a gap in something other than a living body, and it works only because everyone can picture a mouth as a hole that takes things in.
Keep this sense distinct from the next one. Here the mouth is simply the organ, and what matters is that something physically goes into it or comes out of it, not that words are spoken.