Why is sexual reproduction a more important source of genetic variation than asexual reproduction?
Sexual reproduction gets its source of genetic variation from crossing-over and genetic recombination.
As a cell is formed during meiosis in prophase I, each chromosome matches up with its opposite chromosome that is the same size. These chromosomes are both maternal (from the mother) and paternal (from the father). Then, the bottoms of these chromosomes exchange genetic information by replacing the bottom of one of their strand. Here's a picture to help explain:
When a cell undergoes meiosis, it gets either its mother's or father's chromosome for each cell. The chances for each of these is completely random, so it produces genetic diversity instead of it all coming from one parent.
I found this animation that might be helpful: http://www.sumanasinc.com/webcontent/animations/content/meiosis.html