The process by which gametes or the the cells that undergo fertilization are produced is referred to as meiosis. This results in formation of sperm and egg cells in males and females respectively that contain only one copy of the chromosomes. During fertilization, the sperm and egg cells combine and the genome of the resulting cell has all the chromosomes required.
When disjunction does not occur, one of the gametes formed does not have a particular chromosome whereas the other has two of them. If the gamete with a missing chromosome or the one with the extra chromosomes takes part in the fertilization process, the resulting offspring does not have a normal genetic profile. This results in genetic disorders like the one mentioned.
Down's syndrome is the result of an extra chromosome 21 in the genetic profile of the offspring. This is one of the few lethal results of extra chromosomes; usually it is the combination of gametes with a lesser number of chromosomes that leads to disorders in the offspring.