True genealogy requires proof of descent in the form of primary sources (birth records, marriage records, census records, etc). This can be very difficult, and sometimes impossible if the records no longer exist. Most researchers compile an alleged family tree based on secondary sources (family tree books compiled by others, often not well documented) or tertiary sources (the OneWorld Tree or Ancestry World Tree at Ancestry.com, the World Family Tree at Genealogy.com / Family Tree Maker, or the LDS IGI or PAF files) which are themselves compiled from often tertiary, secondary or unknown sources and can be very unreliable.
A DNA surname study helps to prove paternal relationships between cousins. (A "paternal" relationship is one traced entirely through male descent.) The Y chromosome is only passed down to males. Since surnames are traditionally also passed down only to males, a Y-DNA test corroborates paternal relationship between two people, even very distant cousins. This is exciting, because surnames often come in different variant spellings, steering genealogical research in the wrong directions. One surname can end up with very different spellings, or, two completely different names can end up spelled exactly the same even though there is no paternal common ancestry within the last thousand years. The DNA study will tell us who is related paternally.
It also can show paternal relationship between distant cousins with entirely different surnames. This can happen when an ancestor has an adopted or changed name, or if the common ancestor is so far back in time that surnames were not passed down. In ancient days, a surname changed from generation to generation based on occupation (Smith, Carpenter, Baker, etc), location (Marsh, Cullen [meaning "back of the river"], Dunlop [meaning "muddy hill", etc) or descent (Williamson [meaning "son of William"], MacDonald [meaning "son of Donald" in Ireland], O'Brien [meaning "grandson of Brien" in Ireland], FitzRoy [meaning "illegitimate son of Roy"], etc), and so on. Sometimes it is not even very clear. (John Williams may be the son of a William, whose name was William Richards because he was the son of a Richard, whose name was Richard Hughes because he was the son of a Hugh... It's a nightmare for genealogists.)