While the above post is mostly correct (thank you Martikadragoon!!) - In Down syndrome the person has 47 chromosomes instead of the usual 46 which come from 23 pairs of genes (half of which come from mom and other half from dad) the 21st pair has an extra copy (thus the name Trisomy 21). If you research "Down syndrome chromosome chart" you will be able to see this more clearly. People who have Ds usually have certain characteristics, but not everyone has the same ones, but they are common in most. There are different types of Down syndrome or Ds for short. Around 93% have Trisomy 21 which is typically random. 4% have what is called Translocation which is where a piece of genetic material breaks off and attach itself to other genes. 3% has whats called Mosaic Ds which is where not all the cells have the extra material, and sometimes because of this the features are less prominent.
I recommend you visit the Down syndrome group here:
http://www.medhelp.org/forums/Down-syndrome/show/749 (not this community) because I have posted several help files and reference information you may find very handy.
If you have any other questions, please feel free to message me or visit our group for help!
Sandi (Down syndrome Group Founder) aka Dragon1973