What occurs in nondisjunction and what effect does it have on the resulting cells?

Nondisjunction is the failure of a pair of chromosomes to separate (to disjoin) during cell division (meiosis).  When this happens ( in anaphase I of meiosis)  two out of the four new daughter cells produced from a parent cell will have an extra copy of one chromosome and the other two daughter cells will end up missing that chromosome. 

Most of the time when fertilization involves gametes with an abnormal number of chromosomes, the resulting cell does not survive to produce a new individual. However there are some cases where the individuals survive and such, when they are born end up having a syndrome caused by too many or too few chromosomes. An example is Turners syndrome  caused by too few chromosomes  (monosomy x) , and Down syndrome caused by too many chromosomes (trisomy 21).