Why is survival of the fittest misleading?
Most people hear this phrase and assume fitness refers to strength/endurance/health: the way we humans typically refer to our own fitness.
In terms of evolution and biology, fitness has an entirely different meaning. Fitness is an individual's ability to successfully reproduce and have those offspring survive.
Thus, an individual's fitness is not determined solely by strength, although this may play a factor (because the health of an individual is likely to affect reproduction). Fitness is the ability to survive and reproduce viable offspring. The more surviving offspring one produces over a lifetime, the greater the fitness. One's health, luck in finding healthy mates, and ability to raise offspring all potentially have an effect on fitness. There's also a certain amount of luck involved in whether or not one's offspring make it to maturity.
For example, if a very strong lion sires one offspring, he is considered less fit compared to a physically very weak lion that sires ten offspring.
Another example: a cheetah gives birth to three cubs over the course of her lifetime, but none of those animals survive to adulthood and reproduce themselves. Therefore, the fitness of that original cheetah is zero, because her genes were not successfully passed on. The more surviving offspring you have, the more your genes are passed on, the greater your fitness.