What is the connection between the segregation of alleles and meiosis?

This is more of a genetics question than a medical one, but as ever, I'm happy to try to explain.

Mendel's law of segregation is basically that each of an organism's gametes (egg or sperm cell in the case of humans) receives only one allele from each pair of alleles possessed by that organism. When the male and female gametes fuse, the full complement of alleles is reestablished. In other words, every organism has two alleles for each gene, but only one of these is found inside any particular gamete.

This phenomenon is explained by the process of meiosis. In this process, only one CHROMOSOME from each homologous pair goes into each gamete. The important point is that each of the two chromosomes in a homologous pair contain only ONE of the two alleles of a gene. Since the gamete only receives one CHROMOSOME out of each pair, it will therefore only receive one ALLELE out of each pair.