What is mitochondrial inheritance?
The Mitochondrial inheritance is the passage of mitochondrial DNA molecules (mtDNA) to the offspring. All the stock of mtDNA an individual has have come from the mother, the maternal grandmother, the maternal great grandmother and so on, since mitochondria are inherited from the cytoplasm of the egg cell (that later constitutes the cytoplasm of the zygote).
There are numerous genetic diseases caused by the mitochondrial inheritance, like Leber's hereditary optic neuropathy, that leads to loss of the central vision of both eyes, and the Kearns-Sayre syndrome, a neuromuscular disease that causes ophthalmoplegia and muscle fatigue.
The Mitochondrial inheritance is an excellent means of genetic study of the maternal lineage (just like the Y chromosome is an excellent means of study of the paternal lineage).