Explain Charles Darwin's Theory of Evolution

Populations naturally vary. (Think of how people in your class vary in height, weight and other features)
This variation is brought about by inheritance of genetic material from parents. 
In organisms that reproduce sexually, 50% of an individuals genetic make up is inherited from each of its parents. These two separate sources of genetic code recombine during development to form a new, unique code.
The process isn't perfect, and often results in mistakes in the new code, these are called Mutations. Often mutations go unnoticed, however they can sometimes mean that the physical traits of an individual are different from those of the previous generation.
If these changes make the individual better at surviving in its enviroment it is likely to be more successful when it comes to reproducing and passing on its own genes. Therefore, more of the individuals in the following generation will have the favourable trait.
They too will fare better than those that do not possess the trait, and so will have more offspring of their own. The favourable trait therefore becomes more prevelent in subsequent generations until it is the norm for that population.