This is from Darwin, I think. It describes the mechanism of selection in evolution: the organisms that are better adapted to their environments are the ones more likely to survive.
Bady likely hates it because it's often misused, by transforming it in a prescriptive statement (from "the fittest survives" to "the fittest deserves to survive) and/or ignoring that what's considered the fittest depends on the environment (e.g. a fish isn't fit in a dry environment, but a cactus isn't fit in the sea).
Specifically natural selection. Sexual selection is also a type survival of the fittest, but its fitness in attracting mates and assuring survival of offspring, regardless of how well this adapts to the environment. And artificial selection grants survival to the traits the selector wants, again not necessarily favoring environmental adaptations.