DNA shows matches to people currently alive, or who were alive at the time they took a test (apart from very rare cases of DNA having been extracted from remains or artefacts).
It is the research to the link between you and the match (your most recent common ancestors - MRCAs) that determines how far back in time that match "reaches".
How far back you can establish MRCAs is dependent on many variables, including the validity of your research and the strength of the match between you. But it is generally accepted that autosomal DNA will only find matches who share a link with you back to a maximum of about 6 to 8 generations, although often less because, whilst you can expect to find a match to 90% or more of your third cousins or closer relatives, at a distance of 5th cousin (6 generations) you can only expect about 5 to 10% of them to share a DNA match with you.
I have a handful of 6th and 7th cousin matches, one of which takes me back to my 5x GGF 1711-1758. The match to my 6C1R is only 12 cM, which in isolation is not really sufficient to confirm a genuine match, as there is a increased possibility of false matches at that length and lower. But my brother and two other cousins also share that match, albeit at similar or slightly lower match lengths, so I am fairly confident that it is more than just "noise". But the depth and breadth of my tree - i.e. the paper and record based research, allowed me to confirm the relationships between all our matches through historic records.
But DNA alone doesn't prove anything other than that you share a match with another individual who has taken a test. It is the traditional research that you have done or can complete to establish the proven link between you and that match, for which DNA is another piece of corroboration that might prove or add weight to the assertion that your research is correct.
Y-DNA and mt-DNA can take you further back along your father or mother's direct male or female line respectively, but again it is the traditional research that will establish the links between you and any match to a particular ancestor. The DNA match just provides further corroboration of that link.
