It has been known since 1959 that Down syndrome is a genetic condition caused by an apparently random error in cell division - with unknown cause(s) - which results in the presence of an extra copy (or part copy) of chromosome 21.
The parents of Down syndrome children are usually genetically normal. It happens in about 1 in 1000 pregnancies.
Usually when one cell divides in two, pairs of chromosomes are split so that one of the pair goes to one cell, and the other from the pair goes to the other cell. In nondisjunction, something goes wrong and both chromosomes from one pair go into one cell and no chromosomes for that pair go into the other cell.
Most of the time, the error occurs at random during the formation of an egg or sperm. To date, no behavioral activity of the parents or environmental factor is known to cause Down syndrome."
Source US NIH