See also the series of articles beginning with The O'Rourke y-DNA Results.
My sister recently tested the autosomal DNA of a cousin on our mother's side. A person inherits autosomal DNA from both their mother and father, unlike y-DNA which comes only from their father. Autosomal DNA is useful for finding reasonably close relatives, up to third and fourth cousins.
Why would you want to do this? Well, your third cousin is descended from the same great-great grandfather as you are. This isn't as far back as it sounds, as you will see from the examples.
Also, maybe that is as far back as you have been able to trace your family, but the third cousin that you locate has been able to work back farther. This could help an American family locate the place their ancestor emigrated from, say in Ireland or England.
Here are a few of the top matches from the DNA we submitted. FamilytreeDNA estimates that they are third cousins to my cousin:
1. One person who submitted DNA has an email address in Canada. One of the "ancestral names" he included was Carson. One of our cousin's great-great grandfathers on his mother's side was Joseph Carson. He was born in 1818 in Canada, and died in Waterdown, part of Hamilton, Ontario, Canada.
2. Another submitter is named Purcell, but one of his ancestral names is Colgan. My cousin and I have a great-great grandmother named Ann Colgan, who married James Rourke. James lived from about 1779 to 1857 in Ballintur Townland, Co. Down, Ireland.
3. Two of the top matches listed Cunningham as an ancestral name. One of our great-grandmothers was Ann Cunningham from Ballymadeerfy Townland, also in County Down. There was also a submitter named Brian Cunningham who ranked a bit lower on the matches, but said his Cunningham family was from Northern Ireland.
Among the other matches was a man named Magee, another person whose ancestor was born in Newry in 1829, and quite a few Fitzgeralds, including some in Canada and Buffalo.
So you get the idea.
What I didn't find anywhere near the top of the list was anyone named O'Rourke or Rodgers. There were a few, but they were ranked pretty low when sorted by likely matches, how much DNA you shared, etc. Likewise for people who said their family was from Leitrim. That is where the large O'Rourke clan in Ireland was based at one time.
If you need any help understanding all this, maybe this formula will help you. It comes from the Wikipedia article on centimorgans, which have something to do with it all:
Pr[recombination|linkage of d cM] = sum_k=0^infty Pr[2k + 1 crossovers|linkage of d cM] = sum_k=0^infty e^-d/100 frac(d/100)^2,k+1(2,k+1)! = e^-d/100 sinh(d/100) = 1 - e^-2d/100/2
Didn't help you? Me neither.
Continued in The Carsons and the O'Rourke DNA.
The image of a DNA strand comes from Wikipedia:File:DNA orbit animated static thumb.png.