A metaphor is a comparison of two things, without using the words "like" or "as" (a comparison with those words would be a simile). Typically, an author uses metaphor to make writing more poetic and help readers visualize the action or indicate clues about characters, setting, etc.
For example, in "The Most Dangerous Game," the narrator says of Rainsford, "The Cossack was the cat. He was the mouse." This metaphor indicates Rainsford's position of helplessness and being toyed with as he was hunted by Zaroff.
Another example is at the beginning of the story, when the narrator describes the surroundings after Rainsford falls overboard, saying “The lights of the yacht became faint and ever-vanishing fireflies.” This line suggests the finality of Rainsford position (he is definitely not getting back on that ship again), as well as creating a beautiful piece of imagery.
Finally, when Rainsford swims towards the island and hears the "muttering and growling of the sea,” there is a metaphor that compares the sea to a living creature, specifically one that might harm him. Aside for being poetic, this reaffirms how stranded he is on the island; the water will not allow him to escape easily.