What they do is to collect samples and look for similarities for people who live in a given place. So, they look at their samples from, say, England and see if there's some common traits. They then assume that the common traits represent the long-term population. When a new client presents a sample they just look to see if it matches any of their common trait samples. If it does they tell you you have roots in those places.
In fact, you may not because your ancestors might have been those who didn't relocate to England (for instance) and stayed in France or some other place but, since many from their region did relocate to England, there's now a number of people in England who share a particular trait. It's not a precise science; just a statistically good guess.