Short answers, pulled from the story.
Meiosis is a special type of cell division of germ cells in sexually-reproducing organisms that produces gametes, the sperm or egg cells. It involves two rounds of division that result in four haploid cells, each with only one copy of each chromosome.
Human gametes contain one set of 23 chromosomes after meiosis. Diploid human cells contain 23 pairs of chromosomes, 46 in total, and meiosis halves that number so that when an egg and sperm fuse the zygote is diploid again.
Meiosis I is the reductional division that separates homologous chromosomes and halves the chromosome number from diploid to haploid. Meiosis II is the equational division, mechanically similar to mitosis, in which sister chromatids segregate to create four haploid cells.
Meiosis was discovered and described for the first time in sea urchin eggs in 1876 by the German biologist Oscar Hertwig. It was described again at the level of chromosomes in 1883 by the Belgian zoologist Edouard Van Beneden.
Meiosis generates genetic diversity in two ways. The first is the Law of Independent Assortment, the random distribution of chromosomes to each daughter cell, and the second is crossing over, the physical exchange of homologous chromosomal regions during prophase I.
Nondisjunction, the failure of chromosomes or sister chromatids to separate normally, produces gametes with too many or too few chromosomes and is a common mechanism for trisomy or monosomy. Examples include Down syndrome from trisomy of chromosome 21, Patau syndrome from trisomy of chromosome 13, and Edwards syndrome from trisomy of chromosome 18.