This is caused by the addition of genetic material, and in Down's syndrome that's a whole extra chromosome. It happens in cell division (meiosis) during the production of the gametes. Meiosis takes place in the ovaries or testes and 1 cell with 46 chromosomes splits into 2 cells with 23 chromosomes each. This is how sperm and egg cells are produced.
During cell division each pair of chromosomes should separate and travel to specific parts of the dividing cell. This is known as 'disjunction.' However, sometimes the pair does not divide and instead sticks together and travels to its place in the dividing cell. This is known as 'non-disjunction' and the result is that one cell (gamete) will have 24 chromosomes and the other 22.
If such a gamete is used in fertilization, its 2 chromosomal copies are united with 1 chromosomal copy from the normal gamete, which results in an embryo with three copies of that particular chromosome. People with Down's syndrome have an additional copy of chromosome 21.
The effects are different from person to person but include mental retardation, heart defects, a short stature and decreased muscle tone.