N., in some cases, MtDNA has been known to mutate only once in 1,500 years. This means that if you share an exact match with anther woman for MtDNA you can be sure that you have a great-grandmother who is your common ancestor. But is she your 3rd great-grandmother, your 30th great grandmother, or your 300th great grandmother? If two women suspect they are descended from the same 5th great-grandmother (via direct maternal mother-to-daughter descent), an MtDNA exact match says that this is a possibility. Anything less rules it out.
If there is paper showing the two women descend from the same family then the MtDNA would more or less validate it. But two random women, or even two women who lived near each other, all the MtDNA test says is that you shared an ancestor. It is possible that two neighbors who are otherwise unrelated could share an exact MtDNA match if their gggggggggggggggggggggg-grandmothers were the same. In other words, without paper, you can't be sure if the person is your 3rd cousin or your 30th cousin.
My 6th great-grandfather David Abbott had 4 sons. The sons spread out around the time of the Revolution and took up in different parts of America. In the last 30 or 40 years, a lot of Abbotts got together to see if they could determine who was related to whom. Many of these family branches had oral history back to David Abbott and family trees to one of his sons. Some Abbott families had no paper at all and had no idea where they came from.
The men of each family group took YDNA tests and all of the tests were close enough to validate that all of the men from these different Abbott groups came from David Abbott. And those who came from son Richard had distinct markers that the other lines didn't have. Sons of the other brother James had markers that other branches didn't have and so on.
When some of the descendants didn't have any documents at all, by seeing which group they matched we could see from which of David's sons they descended from. This was useful in helping them to narrow their genealogical search knowing where their ancestor (son of David) migrated to. If you have two census records as possible matches for your great-grandfather and you aren't sure which is the correct one, if one is in the same place as David's son migrated to, that's a solid lead.
Image if David's DNA read:
3 of his sons might inherit BBBBBBBBBBBB
and a 4th son gets a mutation BBB1BBBBBBBB
Now, all of the sons of the 4th son will carry that "1"
If a grandson of David's 4th son had a mutation, say a C in the second location, his would look like:
The "1" would let us know that he is a grandson to the 4th son. And all of his descendants will carry BCB1... whereas his brothers might all be BBB1.
More mutations means that you can identify common ancestors in a shorter time period (50 years, 100 years, 150 years), hence, more mutations are more accurate for genealogical searches. MtDNA might show a match at 50 years, at 500 years, or at 1,500 years = less accurate.