Chromosomal abnormalities are the main cause of birth defects afflicting tens of thousands of infants every year. The numbers are pretty scary, about 20% of all conceptions result in spontaneous abortions (usually before the mother knew she was pregnant), and about half of those are due to a chromosomal abnormality. Of all conceptions that do show those abnormalities, 98.4% are aborted, 1% are stillborn, and 0.6% make it to birth alive.
When you consider that between 25 and 30 thousand babies are born with these abnormalities each year in the U.S., that means that there are over a million conceptions with abnormal chromosome configurations! The cellular processes controlling cell division, fertilization, and development are very specific, and the slightest misstep has extremely serious consequences.
The most well-known chromosomal abnormality is Trisomy 21, also called Down Syndrome. Individuals with this disorder have three copies of chromosome 21, instead of the usual two, and this is estimated to be the cause of 1/4 of ALL miscarriages. This results from a nondisjunction when the chromosomes separate in meiosis. Either the sperm or the egg (almost always the egg) ends up with both copies of the chromosomes which were supposed to be divided between the two daughter cells, and after fertilization by the sperm, which has its own Chromsome 21. the baby then has three, giving it a total chromosome count of 47, as opposed to the 46 found in normal humans, resulting in the characteristic abnormalities of the syndrome: epicanthal folds (the politically incorrect reason the disorder used to be called "Mongoloid idiocy"), underdeveloped secondary sex characters, depresssed immune system, heart trouble, simian fold on the palms, and various other health problems resulting in shortened life expectancy.
This is how the vast majority of Down Syndrome cases can be explained. There is, however, a different mechanism that can produce exactly the same disorder. Called "Familial Down Syndrome", it results from a translocation of part of Chromosome 21 onto Chromosome 14. Basically, part of 21 breaks off and attaches itself to 14, but it is a big enough chunk that it retains most of the genes and can function well enough to substitute for the whole chromosome.
So you have a cell with a good 21, and two 14's, one of which has a second 21 latched into it. What happens when the cell divides (goes through meiosis) to make gametes? It is supposed to dole out its chromosomes equally to each daughter cell, but this configuration can't be separated correctly. As a result, you get four kinds of gametes: normal, one with only 14, one with only the 14/21 hybrid, one with a 21 and the 14/21.
Obviously this is a mess, and it gets worse after fertilization. The results are shown below. The blue chromosomes are 21, the pink ones are 14. There are four possible outcomes of a fertilization: you get a normal child, a child that looks normal but carries the mutation, a nonviable zygote (all autosomal monosomies in humans are fatal), or a child with Down Syndrome, which has a 45% chance of surviving to its first birthday.
This fascinating mechanism is the cause of about 3-5% of Down cases, and is an example of the complexities involved in chromosome regulation during development.