During asexual reproduction the parent passes on an exact copy of it's genome to the progeny. This means that it is a clone. Thus in asexually reproducing organisms diversity can only be produced by mutation
During meiosis in sexually reproducing organisms there are two processes that create huge amounts of variation: independent assortment and recombination/crossing over
The meiotic divisions produce cells that have half the number of chromosomes as other cells in an organisms body. This is so that when two sex cells are combined to create offspring the number of chromosomes is maintained generation to generation. For example, we have 23 pairs of chromosomes in most of our cells but our sex cells have only 23 chromosomes
One of each chromosome pair came from our father and the other came from our mother. The sex cells that we produce end up with only one chromosome from each pair, and this is randomised. This comes about because of independent assortment. The variation from this is huge each individual can produce : 2^23 = 8,388,608 different sex cells. Sex with another individual can the produce 2^23 x 2^23 = 70,368,744,177,664 different offspring
What is surprising is that independent assortment is not even where most of the variation comes from. When cells undergo meiosis the chromosome pairs join together briefly before being seperated into different cells. During this time the chromosomes switch pieces of DNA in the process called recombination/crossing over. This happens in numerous places along each chromosome and the locations are (mostly) random. Thus this process can produce variation that is that is as close to infinite as you can get
http://en.wikipedia.org/wiki/Meiosis
http://en.wikipedia.org/wiki/Mendelian_i...