nondisjunction
When chromosomes are being divided up among the cells made in meiosis, each new cell is supposed to get exactly one of each. Nondisjunction is the mistake where a pair fails to come apart, so one cell ends up with an extra chromosome and the other with one too few.
It can happen in meiosis I, when homologous chromosomes fail to separate, or in meiosis II, when sister chromatids fail to separate. Either way, the resulting gametes carry an abnormal chromosome number. If such a gamete takes part in fertilization, the embryo will have an extra or missing chromosome, a condition called aneuploidy.
The consequences depend on which chromosome is affected. Trisomy 21, the cause of Down syndrome, results from an extra copy of chromosome 21; missing or extra sex chromosomes cause conditions such as Turner and Klinefelter syndromes. The chance of nondisjunction rises with the age of the egg cell, which is part of why the risk of certain chromosomal conditions increases with maternal age.
Many embryos with an abnormal chromosome number do not survive to birth, which is one reason such errors are common at conception but rarer among live births. This is a description of biology, not a judgement of any individual; people living with these conditions lead full lives.