Mitochondria contain their own set of genes (this is in addition to the genes in the cell's nucleus). Mutations in the mitochondrial DNA cause several well recognised disorders, often associated with neuromuscular features.
A person inherits his or her mitochondria from the egg and not the sperm. Therefore, mitochondrial inheritance gives a pattern of the condition affecting males and females, but always inherited from a mother. An affected male does not pass on his mitochondria to his children, so all his children will be unaffected.