Mitochondria are complex little buggers which live in our cells almost like little bacteria. They are the cell's, and thus the body's, power source (they burn sugar and only sugar but, only if necessary, the body will convert body fat or body protein into sugar for them to burn). They have their own DNA which is separate from your personal DNA.
"mtDNA" is only inherited from the mother, which is why we know that all living humans are descendants of one woman, Mitochondrial Eve. That is quite remarkable.
In recent years, the identification and understanding of Mitochondrial Diseases has been progressing. Most of these diseases are disabling or fatal: What is Mitochondrial Disease?