Meiosis is the process of creating the Gamete or sex cells (sperm and eggs) that contain 1/2 the chromosomes of the original cell.  It is this process we are most concerned with understanding as part of Genetic Genealogy as this occurs once between each generation.  It is during this process that a change can be introduced.  Meiosis is different than typical cell replication of Mitosis that occurs all the time to keep the overall human body functioning by replacing dying and old cells.  Both start with the process of DNA Replication to create a copy of all the chromosomes — a copy of both strands that are slightly different.  The difference is Mitosis then creates two cells that were identical to the first.  Meiosis creates 4 cells that each only contain one of each strand of the original chromosome pairs.

The only non-nuclear, non-chromosome DNA is the Mitochondria located in the cell body.  This has a different process for replication and is passed, in tact, down to the new cells in both cell division processes.