Lynn Cheney explained in an MSNBC interview:

“This is such an amazing story,” Cheney said in an interview on MSNBC, “that one ancestor, a man that came to Maryland, could be responsible down the family line for lives that have taken such different and varied paths as Dick’s and Barack Obama’s.” Cristina Allegretto, Mrs. Cheney’s research and project manager at the American Enterprise Institute, said the vice president’s wife did an exhaustive genealogical search of her family while working on “Blue Skies, No Fences.” Her research led her to an early Cheney settler named Richard Cheney, whose granddaughter married Samuel Duvall, whose mother, Mareen Duvall, is distantly related to Obama. Lynne Mrs. Cheney read a story that said Obama was related to Mareen Duvall, and realized the link.

Obama, whose mother was white, did not immediately comment on the revelation. But his campaign made light of the tie, without confirming it. “Obviously, Dick Cheney is the black sheep of the family,” Obama spokesman Bill Burton said.

ThinkProgress has the video.

And the Chicago Sun Times elucidates further:

Obama and Bush are 11th cousins.

That’s because they share the same great-great-great-great-great-great-great-great-great-great grandparents — Samuel Hinckley and Sarah Soole Hinckley of 17th century Massachusetts.

That means Obama and former President George Herbert Walker Bush are 10th cousins once removed. Obama is related to Cheney through Mareen Duvall, a 17th century immigrant from France.

Mareen and Susannah Duvall were Obama’s great-great-great-great-great-great-great-great-great grandparents and Cheney’s great-great-great-great-great-great-great-great grandparents.

That makes Obama and Cheney ninth cousins once removed.