Crossing over is when material is exhcanged between homologouges (meiosis). Homologous portions of two non-sister chromatids trade places (cross over). This produces chromosomes that contain genes from both parents. Interestingly enough, human beings have an average of 2-3 crossovers PER chromosomal pair. With this taking place, then, one can see that the genetic variation in offspring would be wide, and this is a good thing as it keeps mutations (of the bad sort) from expressing themselves.