Populations can produce far more offspring than the environment can support, so individuals compete. Those with the best adapted phenotypes are more likely to survive, reproduce and pass on their alleles. Over generations the frequency of these alleles rises. This is natural selection.
Selection can keep the average (stabilising), push the population towards one extreme (directional) or favour both extremes (disruptive). Allele frequencies can also change by chance. This is genetic drift, and it is strongest in small populations, such as founders of a new population or survivors of a bottleneck.
In selective breeding humans choose the parents, generation after generation, to improve a feature they want.