The basic premise is that you look at mutations, and, through statistical analysis, you have a general idea of when and where certain mutations occurred.
All births come with a certain frequency of mutations, which are often unique. If you and I are fourth cousins, and our great-great-great-grandfather was born with some normal benign mutation, the chances are good that both you and I would share that mutation, and that other people won’t. By noticing that mutation you could tell that we are more closely related to each other than either of us are to our fifth, or tenth cousins.
With tens of thousands of people, you can do statistical analysis and have a good guess as to when and where certain mutations took place. You can discover that, say 99% of Caucasians have a mutation that occurred in the Urals x-thousand years ago, that 99.9% of Native Americans have a mutation that took place in Siberia y-thousand years ago, and that 90% of South-East Africans have a mutation that took place in Mozambique after other groups left the area.
So this is what they are calculating. If you have one of those mutations that took place in Sub-Saharan Africa just 5,000 years ago, then you must have at least one ancestor that came from Sub-Saharan Africa in the last 5,000 years. If you have many of these mutations, then chances are high that a greater proportion of your ancestry came from Sub-Saharan Africa.
As for this case, of course it’s a little strange just to say “14% Sub-Saharan African” because if you go far back enough, everyone is 100% Sub-Saharan African. But what this means is 14% ancestry that has unique mutations that are found in more recent Sub-Saharans and not in the peoples who left for Europe.
