Crossing over occurs during meiosis. When homologous chromosomes are aligned and they stick together by the chiasma point. At this point, the homologous chromosomes chains break and get recombined with the broken portion of its homologous. The result is that one of the progenitor´s chromosome will have a portion of the other progenitor´s chromosome, and vice-versa.
If crossing-over does not occur, the independent assortment of the homologous chromosomes in a cell will produce two different genotypes that equals the ones of the progenitors. So, there will be two genotypes, one of them equals the female´s genotype and the other is like the male´s genotype.
