You can get chromosomal abnormalities occuring during meiosis. Sometimes when the pairs of homologous chromosomes split up one of the daughter cells ends up with both of the pair and the other daughter cell has none. The cell that ends up with none is usually not viable, but the other (if it results in a pregnancy) can cause a trisomy, where the baby has three copies of a particular chromosome, instead of the usual two.
Trisomy 21 (when there are three copies of the 21st chromosome) results in Down's syndrome. This is probably the most widely known trisomy.
Other types of trisomy include Klinefelter's syndrome, where a person has XXY instead of the usual XX or XY sex chromosomes, and XXX syndrome, where the affected person has three x chromosomes. People with XXX syndrome are generally indistinguishable from normal females - it is quite possible that they can spend their whole lives without ever being diagnosed.
There is also Turner's syndrome, which is not a trisomy, but results from a delection of one of the X chromosomes (it is the only monosomy that can result in a viable foetus, as far as I know).
If you want to look up more info, you should google "aneuploidy."