Good for you for getting going and sharing this hobby with your son. I think it is a great thing to share between generations.There are three types of DNA tests genealogists use, Y-DNA only men have and traces the paternal (surname) line back to pre-historic time, well before names were used. Women can do the MTDNA test that traces only your mother to her mother to her mother back forever. The most useful one for discovering genealogy is an Autosomal DNA test which men and women can both take.
The Family Finder test , 23 and me, Ancestry autosmal tests use autosomal DNA which can trace both your male and female lines from all four of your grandparents. It works for both women and men equally as we both have it. It can detect the DNA you inherited from generations of grandparents on both sides but only for about six to seven generations back getting smaller each generation if it passes at all then it starts disappearing and getting too small to detect. You can tell by the length (which is measured in "centimorgans") of shared DNA shown on a diagram of the 23 chromosomes how recent the ancestor was. They show the diagrams on Family Tree family finder or 23 and me or gedmatch.com which takes the raw DNa from other groups for free and compares them with a tool that shows which chromosome you match on. Ancestry doesn't have that tool but shows you after you load your family tree who else shares DNA with you AND who you both have in your tree. One has to have a written family tree that includes the husbands and wives which grows exponentially every generation to a very broad group of people at six generations in order to make successful matches that are further back, you start by contacting the largest matches you show if they have the surname of one of your parents, grandparents or great grandparents.
There is another type of DNA test which can only trace your maternal line and it is called a MTDNA test. That is what you are describing. Some people mistakenly think that the M stands for maternal DNA but the "M" actually stands for "mitochondrial" which, like the Y-DNA is a special female DNA that doesn't change and is passed from mother to daughter. MTDNA is not very useful for finding cousins because only those few people who are daughters and sons of the same mothers in your line will share that with you.
The MTDNA test also showswhere your female ancestors came from back in pre-history (your "EVE") and it has a special designation called a haplotype . Your haplotype is: U5b and if you look it up it there will be information on wikipedia about that group's migration from Africa across other continents. If you want to find ancestors I think using Ancestry.com is the easiest way to start, but there are some other free groups you can find too. You have to get a little of your tree down before DNA helps is what I am trying to say in this long winded spiel. After that other people are helpful. There are also some facebook groups for whatever genealogy testing service your son used that have people that can help too. Good Luck!