The mitochondria in the cells descend from the mitochondria in the oocyte of the mother. They contain DNA and form a maternal extra-nuclear inheritance. This DNA is called mt-DNA and can be used to trace female genetic lines in pedigrees.
They Y-chromosome is only passed from father to son. The DNA on this chromosome is called Y-DNA, it shows no crossing over and can be used to trace male genetic lines in pedigrees.