Asexual reproduction is a form of reproduction, which only involves one parent. Plants for example use asexual reproduction or in their case vegetative reproduction. Vegetative reproduction is when parts of the old plant fall off and develop into new plants. The new plants will grow very close to each other and to the parent. This will cause a struggle for soil, nutrients and light, and will consequently cause the plants to be less healthy. During asexual reproduction there is no chance of an evolution occurring, the offspring would almost always be of the same species and would be identical to the parents, so diseases are also passed down directly from the parents to the offspring.
Sexual reproduction is reproduction involving the union or fusion of a male and a female gamete. During sexual reproduction is that there is a large chance of an evolution-taking place. The new species will be able to adapt to environmental conditions, and the new character that is formed with the mixed gametes of the parents so there is a chance that the parent’s diseases would not be received by the offspring.
Sexual reproduction is important when talking about evolution because it also facilitates the increase in fitness under natural selection, leading to the 'best' combinations of genes. Sex can impede the increase in the fitness of the population the how it can remain the dominant form of reproduction across all manner of species. Sex at its foundation of merging of genes from different individuals creates genetically unique genes. If the goal is to maximize fitness by finding a particularly good combination of genes, asexual reproduction - which increases a population's numbers at a much faster rate than sexual reproduction works pretty well.
University of Iowa. "Value of Sexual Reproduction Versus Asexual Reproduction." ScienceDaily, 25 January 2010. Web. 15 November 2010. http://www.sciencedaily.com/releases/2010/01/100121161238.html
Ridley, Matt. "The Advantages of Sex." 4 December 1993, Print. http://www.pbs.org/wgbh/evolution/sex/advantage/index.html