Explain the theory known as “survival of the fittest”

The "Survival of the fittest" statement has been around for quite some time. 

The theory of it is quite literally how it sounds. Only the strongest, fastest, most intelligent, and best of a respective group shall truly survive. 

This theory is practically how the entire food chain works. You have Predators, and you have Prey. The Predators are the strongest, fastest, and best of their food chains, and the one at the top is the one who's known as the "Apex Predator". The best of the best. Now, amongst the prey, you'll always have some more fit to survive than others. For instance, an eagle vs an armadillo. The eagle is fast, strong, with deadly sharp claws, a pointed beak made for piercing, and eyesight better than nearly anything. The armadillo is slow, chunky, but also heavily armored. 

Of the two, the eagle is more fit to survive. It doesn't matter how heavily armored you are, eventually -granted your opponent is strong and determined enough- will wear the armadillo down, and get the better of it eventually. The eagle was more fit to survive. 

Ever heard of the statement: "I don't have to outrun THEM. I just have to outrun YOU". Yeah, well as harsh as it sounds, it's the same concept. 

The theory holds that only the best of the best of each specific class or category shall survive, thrive, and excel. Only the most determined of the determined, the ones who want to survive the MOST. Of course, peak physical and mental shape is of great importance. 

~Hope this helps