Natural selection is a process in which organisms who are better adapted to their environment tend to have better chances of survival and produce more offsprings. 

Organisms with the advantageous alleles are better adapted to their environment. These organisms then reproduce and pass on these advantageous alleles to their offspring. This eventually leads to evolution. 

Natural selection helps us to understand evolution better and gives us an idea why organisms are of different shapes and sizes. 

Example: 
Let us say that in a park, there are green worms and red worms. 

The green worms can camouflage in the green grass but the red worms will stand out. The predators will then eat the red ones as they are easier to spot. 
The green worms will survive because they have the advantageous allele which gives them their green colour. They will reproduce and pass these advantageous alleles to their offspring. 

In the example above, the green colour and the red colour of the worms are their phenotypes.
A phenotype is a visible characteristic of an organism which comes about as a result of their genes. 

Natural Selection was first expounded by Charles Darwin. 

The Process

1) Mutation
Differences in DNA in individuals of the same species arise.

2) Variation
Physical differences in individuals of the same species arise. 
e.g. some worms are green and some are red

3) Competitive Advantage
Some individuals become more adapted to their environment. They outcompete others for resources.

4) Survival of the Fittest
Those that are more well adapted to their environment have better chances of survival.
e.g. green worms are more likely to survive in a park than red worms

5) Reproduction
Those that are better suited to their environment have more offspring.

6) Passing advantageous alleles
Those that are more well adapted to their environment are able to pass on their advantageous alleles to their offspring. Therefore, their offspring are also better suited for their environment.