Nemesis is only mentioned in one measly line of the Echo and Narcissus myth, so she isn't really a character in the traditional sense. But still, she's responsible for Narcissus' death, so we'll give her some Shmoop screen time.
In some versions of mythology, Nemesis is the daughter of Erebus (darkness) and Nyx (night). Spooky. Other myths suggest that the Titan, Oceanus, was her father, and still others blame Zeus. Regardless, her role in ancient Greek culture remains the same. Nemesis is the goddess of divine retribution. Her job is to make sure that no one is too happy or too lucky.
This lady gets especially angry at people who have great fortune but don't deserve it. But we can't forget that she can be equally kind to people who suffer great tragedy for no reason. Basically, her goal is balance.
Also, the word nemesis should sound familiar: this lady gave her name to the word we use today to describe someone who's out to get us.