A mechanism of evolution that leads to non-random spread of genes due to the effect that genes have on reproductive success.

Selection is an important mechanism of evolution which brings about changes in gene frequencies by inducing variance in reproductive success as a direct result of the genes possessed. Selection is the mechanism of evolution which underlies the process of adaptation.

Darwin theorised that evolution could occur by natural selection in the 1800's, based on the idea that variance in heritable phenotypic characteristics could have a direct effect on reproductive success. As such, individuals that posses genes which give them an advantage in reproduction should (assuming selection is constant between generations) also produce offspring of a higher fitness, and the offspring generation would more closely resemble that individual than the parental generation did.

A classic example is the peppered moth. Before the industrial revolution most peppered moths were light in colour. Pollution from the industrial revolution caused the darkening of the environment. This gave an advantage to peppered moths that possessed genes causing a darker colouration, because predators were less able to spot them relative to lighter moths. The genes for dark phenotypes then spread through the population because these individuals were able to produce more offspring.

Questions about how selection works, the effect of selection, population genetic interactions, and interactions with other mechanisms of evolution are generally on-topic. Subjective questions about the validity of evolution by selection are generally off-topic. Before asking why a seemingly advantageous trait has not evolved see this post. Understanding Evolution is a particularly useful introductory source and includes a large myth-busting section.