Barack Obama Sr. was a native of Kenya and therefore a British subject until 1963, when Kenya formally gained its independence. At that time, he became a Kenyan citizen.
Barack Obama Jr. was born in Hawaii but had dual U.S. and British citizenship because of his father. The younger Obama then became a dual citizen of America and Kenya, but that expired when he turned 23 because Kenya forbids dual citizenship for adults. Citizens of Kenya who also have citizenship with another country must renounce the other country and swear allegiance to Kenya, or else they lose their Kenyan citizenship.