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Recall that somatic cells are body cells excluding the reproductive cells. For example, this includes cells of the liver, skin, stomach, but not of sperm or the human egg. In contrast, germ cells are cells which contain half the number of chromosomes when compared to a somatic cell. The reason why they have half the number of chromosomes is that when they unite with another germ cell (gamete), they form a zygote with $2n$ chromosomes, which is the correct number of chromosomes required to produce a new and viable organism.

Crossing over occurs in meiosis and not in mitosis because meiosis is the process whereby alleles are exchanged in order to create diversity between organisms. This is why everyone looks different — the crossing over of alleles in gametes makes new genetic combinations. Daughter cells created during meiosis are non-identical. In contrast, mitosis creates daughter cells which are identical to the parent cell.