The mechanism for evolution is natural selection. Natural selection is the process that decides which adaptations for a given environment are favorable and which are not as desirable. If a trait is the favored adaptation, then individuals that have the genes that code for that characteristic will live long enough to reproduce and pass down those genes to the next generation.
In order for natural selection to work on a population, there must be diversity. To get diversity in the individuals, genetics need to be different and different phenotypes must be expressed. This is all dependent upon the type of reproduction the species undergoes.
Asexual reproduction is the creation of offspring from one parent. There is no mating or mixing of genetics in asexual reproduction. Asexual reproduction results in a clone of the parent, meaning the offspring has identical DNA as the parent. There is usually no variation from generation to generation in a species population that relies on asexual reproduction.
One way for an asexually reproducing species to get some diversity is through mutations at the DNA level. If there is a mistake in mitosis or the copying of the DNA, then that mistake will be passed down to the offspring, thereby possibly changing its traits. Some mutations do not change the phenotype, however, so not all mutations in asexual reproduction result in variations in the offspring.
Sexual reproduction happens when a female gamete (or sex cell) unites with a male gamete. The offspring is a genetic combination of the mother and the father. Half of the offspring's chromosomes comes from its mother and the other half come from its father. This ensures the offspring are genetically different from their parents and even their siblings.
Mutations can also happen in sexually reproducing species to further add to the diversity of the offspring. The process of meiosis, which creates the gametes used for sexual reproduction, has built in ways to increase diversity as well. This includes crossing over, which ensures the resulting gametes are all different genetically. Independent assortment of the chromosomes during meiosis and random fertilization also add to the mixing up of genetics and possibility of more adaptations in offspring.
Reproduction and Evolution
Generally, it is believed that sexual reproduction is more conducive to driving evolution than asexual reproduction. With much more genetic diversity available for natural selection to work on, evolution can happen over time. When evolution does occur in asexually reproducing populations, it typically happens very quickly after a sudden mutation. There usually is not a long time of accumulating adaptations like there is in sexually reproducing populations. An example of this relatively quick evolution can be seen in drug resistance in bacteria.