There are two places in a
cell where
DNA is stored: the vast majority of it is in
chromosomes in the
nucleus; but a small amount is in each
mitochondrion, the energy factories scattered around the cell. All
multicellular and some single-celled
organisms have this distribution: they are called
eukaryotes.
The nuclear DNA and the mitochondrial DNA are independent of each other. The mitochondria are believed to have originally been free-standing organisms that entered into symbiosis with the nuclear cell: so are the chloroplasts, a third place in plants and some other eukaryotes that also has independent DNA. The chromosomes are divided and both parents contribute to their offspring's chromosomal DNA (in those species which reproduce sexually, which is almost all). But any mitochondria in the sperm cell are gone by the time it is fused into the ovum, so only mitochondria from female cells are passed onto the next generation.
Humans have 37 genes in their mitochondria, in a total of only 16 569 base pairs. Compare this to the genome in the chromosomes, estimated as anywhere between 35 000 and 150 000 genes. (I don't know what the latest estimate from the Human Genome Project is, but any of these figures dwarf 37.) [Update 11 Feb.: between 26 000 and 40 000 according to figures released today.] All the genes are essential. Nevertheless it does mutate like any other DNA, and sequences can be compared to determine parsimonious trees of presumed descent.
Because mitochondrial DNA, or mtDNA, is inherited through the maternal line, it is never diluted by sexual recombination, and if it mutates at a fixed rate, that may be used as a molecular clock to estimate actual ages of divergence of the lineages obtained. Scientists have attempted to calibrate the clock by looking at isolated populations where the date of arrival can be checked archaeologically; and on the other side of the scale by comparing humans to chimpanzees.
When this was done in 1987 it gave rise to the Out of Africa theory, which already exists as a node, so I won't go into it here. The mtDNA evidence suggests the common maternal ancestor of all modern humans lived between 150 000 and 250 000 years ago, in Africa (because African DNA is by far the most diverse): this common ancestor is called Mitochondrial Eve (another existing node I'm not going to duplicate here).
There are some problems with mtDNA study: the molecular clock has been called into doubt as wildly unreliable; there was a 1991 study showing paternal mtDNA could survive sexual fusion; and a 1999 study even suggested paternal and maternal mtDNA could undergo sexual crossover.
Omigod I've just looked at Out of Africa and it's a one-and-a-half line write-up of the Karen Blixen book. There are also no write-ups for nuclear DNA and multiregional... Feel free to beat me to them. (Update: I've done Out of Africa now.)