Mitochondrial haplogroups are defined by sets of genetic variants that distinguish one major maternal lineage from another. They trace back to specific ancestral lineages in human prehistory. Haplogroup J traces its origins to the Middle East and spread into Europe during or after the Neolithic period, probably carried in part by the agricultural populations that expanded from southwest Asia into Europe beginning around 9,000 years ago.
In contemporary European populations, haplogroup J and its sub-branches are relatively uncommon, typically representing around five to ten percent of individuals depending on the specific region. It is more common in some areas than others, with somewhat higher frequencies in the British Isles than in some continental European populations.
The significance of haplogroup J in the Richard III case is not the haplogroup designation itself — knowing that he belonged to haplogroup J tells us relatively little about him as an individual — but the specific sequence within that haplogroup that was found in both the skeleton and the living comparators. The complete mitochondrial genome contains over 16,000 base pairs, and the specific combination of variants found in the Leicester skeleton was not represented among more than 26,000 complete European mitochondrial genomes in the comparison database.
This rarity is what makes the match between the skeleton and the Ibsen comparators meaningful. If haplogroup J were common, or if the specific sequence were common, the match could be attributed to coincidence. The fact that the specific sequence is rare means that a coincidental match — two individuals sharing the sequence through some pathway unrelated to the documented genealogy — is extremely improbable.