Y-chromosomal Aaron is the name given to the hypothesised most recent common ancestor of many of the patrilineal Jewish priestly caste known as Kohanim (singular "Kohen", "Cohen", or Kohane). In the Torah, this ancestor is identified as Aaron, the brother of Moses. The hypothetical most recent common ancestor was therefore jocularly dubbed "Y-chromosomal Aaron", in analogy to Y-chromosomal Adam.
The original scientific research was based on the discovery that a majority of present-day Jewish Kohanim either share, or are only one step removed from, a pattern of values for 6 Y-STR markers, which researchers named the Cohen Modal Haplotype (CMH). However it subsequently became clear that this six marker pattern was widespread in many communities where men had Y chromosomes which fell into Haplogroup J; the six-marker CMH was not specific just to Cohens, nor even just to Jews, but was a survival from the origins of Haplogroup J, about 30,000 years ago.
More recent research, using a larger number of Y-STR markers to gain higher resolution more specific genetic signatures, has indicated that about half of contemporary Jewish Kohanim, who share Y-chromosomal haplogroup J1c3 (also called J-P58), do indeed appear to be very closely related. A further approximately 15% of Kohanim fall into a second distinct group, sharing a different but similarly tightly related ancestry. This second group fall under haplogroup J2a (J-M410). A number of other smaller lineage groups are also observed. Only one of these haplogroups could indicate ancestry from Y-chromosomal Aaron.
The J1e and J2a possible Cohen clusters, when including those tested who are of Sephardi background, have been estimated as descending from most recent common ancestors living 3,200 ± 1,100 and 4,200 ± 1,300 years ago respectively. Ashkenazis only have been estimated by the same article as descending from most recent common ancestors living 2,400 ± 800 and 3,800 ± 1,200 years ago respectively.
Read more about Y-chromosomal Aaron: Background, Genetic Studies, Cohens in Other Haplogroups, Does A CMH Prove Cohen Ancestry?, Higher Resolution, Other Carriers of The DNA, J2 Kohanim Haplotype Tree, Y-chromosomal Levi, Samaritan Kohanim