How can a mutation led to variation

Mutations produce random changes in an organism's genetic code. Mutations can occur in non-reproductive cells and then they will not be passed to the next generation, therefore will not contribute to variation. Only mutations that occur in reproductive cells are passed on to the next generations and contribute to genetic variation in a population.

Mutations lead to genetic variation by producing random changes in an organism's genetic code.

This causes a different protein to be produced, or none at all. Usually has a negative effect, due to an important protein, e.g. an enzyme, not being produced, so the organism cannot do a certain thing (e.g. digest fats), occasionally makes an organism better able to survive (positive effect). This means that it is more likely to survive and pass the mutated (beneficial) gene on to it's offspring.