The Red Queen alludes to a character in the novel, Alice In Wonderland. In the novel, Alice chances upon a queen running along, who implores Alice to run faster. No matter how fast Alice runs, however, she stays in the same place because the landscape is moving at the same pace she is. This metaphor is meant to suggest a treadmill in a world where no matter how fast one runs, they remain in the same place.
The Red Queen: Sex and the Evolution of Human Nature