Based on these ideas, Darwin proposed the theory of 'Natural selection', which means that the nature only selects or decides which organism should survive or perish in nature. This is the meaning of survival of the fittest. The organisms with useful traits will survive. If traits are not usefull to organisms then they are going to be perished or eliminated from its environment.
Alfred Russel Wallace also independently concluded that natural selection contributed to origin of new species. For example we have seen in the case of red beetles which were seen and eaten by crows. So, the population of red beetles gradually got eliminated or perished from its environment. But at the same time the beetles which are green in colour which are present on the green leaves were not noticed by crows. So the green beetles survived in the environment and their population have gradually increased. This is nothing but “natural selection".

Variations which are useful to an individual are retained, while those which are not useful are lost. In a population when there is a struggle for the existence the 'fittest' will be survived.
Nature favours only useful variations. Each species tend to produce large number of offsprings. They compete with each other for food, space, mating and other needs. In this struggle for existence, only the fittest can survive.
This is called 'survival of the fittest'. Over a long period of time this leads to the formation of new species.
You may observe in your surroundings some seedlings and some of the animal kids only survive. Discuss in your class based on those examples to understand survival of the fittest.
Darwin's theory of evolution in a nutshell1. Any group of population of an organism develops variations and all members of group are not identical.
2. Variations are passed from parent to offspring through heredity.
3. The natural selection over abundance of offspring leads to a constant struggle for their survival in any population.
pg.no.183