Remember that the ordinary cells of the body have 46 chromosomes in 23 pairs. The members of each of the pair don't contain the same genes (this is why you can carry a gene for recessive inheritance without being sick, but if you have both genes there's trouble). During the cell divisions that produce the germ cells (the process of meiosis), the 46 chromosomes first double to 92 before they end up with the 23 present in an egg or a sperm. Two of the four sibling chromosomes (we call them chromatids) then randomly exchange bits of themselves: there's a "cross-over". The points of junction where this happens are called chiasmata. Nature is jumbling up where the genes will end up so that in the long run you don't always have to inherit two particular genes together just because they live next door to each other on a chromosome. Cross-over does not mean that genes can end up in any chromosome they like: unless "translocated", they will remain in pairs (of alleles) within a particular pair of chromosomes. Chromosomal crossover is the origin of what geneticists call hybrid vigor.

Failure of chromatids to separate after chromosomal cross-over during meiosis. The origin of aneuploidy. More common in eggs, or oocytes, than sperm, and increases with age in women.

Read chromosomal cross-over first, then come back. Because it can take lots of cross-overs (i.e. lots of generations) to send two genes that live as neighbours on a chromosome into different directions (i.e. they end up in different people), we can do family studies to work out how closely people are related by seeing how long the runs are of identical genes.