Crossing over allows genetic variants on the same chromosome to evolve independently, which greatly increases an organism’s evolutionary potential.
If there were no crossing over, all genetic variants on a chromosome would be inherited as a block. Image a chromosome copy which contains a good variant–let’s say, flu resistance–at one gene, and a bad variant–let’s say, tapeworm susceptibility–at a different gene. Without crossing over, the population has to choose between flu and tapeworms. Crossing over can produce a chromosome with the good variant and without the bad one, allowing the population to move toward a better solution. This speeds up the rate of adaptation.