Down's syndrome means three copies of chromosome 21. To answer this, rank the ways an extra chromosome 21 can arise by how often each happens.
The dominant mechanism, in roughly 19 of every 20 patients, is nondisjunction during meiosis. When chromosome 21 fails to separate, one gamete carries two copies and, after fertilization, the child ends up with three. Crucially, this error happens chiefly in the maternal egg, especially in the first meiotic division, and becomes more likely as the mother gets older. That is why maternal nondisjunction tops the list.
The remaining causes are minor. Paternal nondisjunction is uncommon. A Robertsonian translocation contributes only a small share but matters for genetic counselling because it can run in families. Mosaicism, where only some cells are trisomic, is rarest of all.
Putting the numbers together, the leading cause of trisomy 21 is failure of chromosome separation on the mother's side.
\[\boxed{\text{Maternal nondisjunction}}\]