A simile is a comparison of two dissimilar things that share similar characteristics, as if they were the same—using "like" or "as" in the comparison.
For example, "You are the sunshine of my life" is a simile, comparing "you" (let's assume it's a woman) to "sunshine." While they share similar characteristics (both can make the speaker feel warm and happy, like the sun does), "she" will never give someone sunburn. It is not literal but figurative language—language not to be taken literally. It's a form of imagery that provides a description of a person or thing the reader may not know to something that the reader does know —in this case, the "sun."
In the story, "The Most Dangerous Game" by Richard Connell, one of the first similes is something that evokes an extremely clear mental image. Whitney is describing the "moonless Caribbean night" and notes:
It's like moist, black velvet.
Note the use of "like," comparing the night to a heavy wet material (velvet). This description gives the reader (without being there) the sense that the air is thick, and it's hard to breathe.
Later Connell provides another simile:
The sea was as flat as a plate glass window.
This compares the surface of the water to the slick and smooth surface of glass, using (in this case) "as" for the comparison of the two.
When Rainsford meets Zaroff the first time, the author uses a simile to describe the General's appearance:
...his thick eyebrows and pointed military moustache were as black as the night from which Rainsford had come.
Once again, the night is used as part of a description; this time the black night is compared to Zaroff's facial hair.
Figurative language—using figures of speech—helps to provide vivid mental imagery for the reader. A simile is one of many literary devices used for this purpose.