Freema Agyeman was born in 1979 in London of Iranian-Ghanaian parentage. She made an appearance in the Crossroads Revival in 2003 (as one of the hotel staff) and like many a British actor, has been in The Bill (in her case, three times as two different characters).
However, her most famous role at the moment is in Doctor Who and later in spin-off show Torchwood. Performing a You Look Familiar, she played Adeola Odoshi in "Army of Ghosts", where she ended up put out of her misery by the Doctor. Three episodes later, in "Smith and Jones", she made her first appearance as med student Martha Jones (a character described inaccurately as "the first black companion", a title that actually goes to Mickey Smith in the TV show -- she was just the first to get billing in the opening credits). The character's similarity to Adeola was later Handwaved by saying that she was Martha's cousin.
Also a star of Law and Order UK, alongside co-Sci Fi Actor Jamie Bamber. And former Doctor Peter Davison. Will play Larissa, mentor to the young Carrie Bradshaw (Anna Sophia Robb), in the Sex and the City prequel The Carrie Diaries.
Is not "African American", nor are any of the characters she's played. She has played black Brits though -- such as Alesha Phillips.