Mutation is a process that randomly modifies a DNA sequence. DNA modification is not always repaired by the cell and it may be passed down to the next generation.
Mutation gives rise to different versions of the same gene. These new versions are called alleles. These new alleles are often deleterious, or harmful to the fitness of the organism, but could also increase the fitness of the individual or have no effect on fitness.
When new alleles appear, sexual reproduction and meiosis combine these different alleles in random combinations, increasing genetic variation. Some of the new genetic combinations will allow individuals to better survive in their environment, and so reproduce more and pass that trait on to their own offspring.
These are the two components of evolution by natural selection - genetic variability leads to differential reproductive success. Without mutation on a molecular level, we see no evolution by natural selection.