B.Sc

Crossing-over occurs in Prophase I of meiosis.
During crossing-over, homologous chromosomes line up along their length, intersect a section of their chromatids, and exchange corresponding parts of that chromatid with each other. So in the end, one of the homologous chromosomes has a segment of the other homologous chromosome's DNA, and vice versa.
Keep in mind that the DNA they exchange codes for the same thing; the genes that are on the DNA code for the same traits as well.
Genetic recombination occurs in Anaphase I of meiosis. The homologous chromosomes are separated, and each resulting daughter cell has one of each pair of homologous chromosomes. However, the combination of what cell gets what chromosomes is completely random- for instance, pretend a parent cell has two pairs of homologous chromosomes; in the first pair, both are large, and one is green and one is blue. In the second pair, both are small and one is green and one is blue.
During Anaphase I, the pairs separate- each daughter cell gets one big and one small chromosome. The "recombination" is that which chromosome the cells get is completely random. It could be that one cell gets the big green, small blue- or the big green, small green- or the big blue, small green- or the big blue, small blue. There are so many combinations. which makes for much genetic variation!