How does crossing over in meiosis result in genetic variation?

Crossing over happens in prophase I when the logous chromosomes are synapsed. The two inner chromatids exchange sections with each other. This means that after the exchange the two inner chromatids have new combinations of alleles than their parents had. The two outer chromatids still have the parental combinations. So there are more kinds of chromatids ready to go into the gametes than there were before. This is an increase in variation.