The Khazar hypothesis is an argument that Ashkenazi Jews are not ethnically Jews, but descended from the Turkic Khazar Empire.
The purpose of the Khazar myth is to create a fictional separation between the modern Jews living in Israel and their ancestral heritage in that land. This is specifically for the purpose of stripping Ashkenazic Jews of personhood and nationhood.
Medical studies of the DNA of various diaspora Jewish populations — from Iranian, Iraqi, Syrian, Italian, Turkish, Greek, and Ashkenazi — have shown them to all be close Middle Eastern kin (source: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3032072/).
These Jews were also compared not only with one another, but with surrounding non-Jewish groups and found that their are distinctive Jewish population clusters — each with shared Middle Eastern ancestry, proximity to contemporary Middle Eastern populations, and variable degrees of European and North African admixture. The Ashkenazim were found to have mixed, about 1500 years ago, with European women, but not much with any native European Y chromosomes (source: http://www.sciencedaily.com/rele…/2013/10/131008112539.htm)
What’s completely absent from these findings is the Turkic DNA, which would have originated with the Khazars.
Though Ashkenazim are the largest ethnic group of Jews today, Sephardim and Mizrahim also consist of a significant part of the Jewish population, both in Israel and in the diaspora. Additionally, Israel has become the home of many smaller Jewish ethnic groups, such as Ethiopian Jews, Yemenite Jews, and Kaifeng Jews. The Khazar myth does not address these populations in Israel at all.
If you bump into the Khazar myth, make sure to refute it.