I can find patterns by comparing DNA sequences of lots of different people with one another.
Usually, you find that people that are more closely related have more similar DNA.
So you and your friends who have Irish ancestors would be more closely related than a group of kids from, say, Kenya, who have African ancestors.
We find that African DNA sequences are very rich! People who have descended from ancestors in the Western World have quite similar DNA sequence data since we tend to have descended from a common ancestor when humans moved out of Africa about 60,000 years ago!
When you look at the DNA sequences through a mathematical model, you can quantify how different these sequences are (what I mean by that is calculating a number that describes the differences).