Taylor was born in Dallas, Texas, but starting at age 12 she went to a newly integrated school in Muskogee, Oklahoma, where she was subjected to an incident of racism by another student.The family later returned to Dallas, where she graduated from L. G. Pinkston High School in 1977.
Her earliest professional acting roles were two made-for-television films while she was studying at Southern Methodist University: 1980's Nurse and 1981's Crisis at Central High. In the latter movie, she was praised by critic John O'Connor of The New York Times for her portrayal of Minnijean Brown, a member of the Little Rock Nine, a group of African-American students who braved violence and armed guards to integrate Little Rock Central High School in 1957. Her first role to gain widespread attention was that of Mrs. Carter, the drug-addicted mother of a promising young female student, in the 1989 film Lean on Me. She became well-known to the television viewing public for her role as Lilly Harper on the early 1990s TV series I'll Fly Away. This role won her a Golden Globe award for Best Actress in a Television Drama and also an NAACP Image Award for Outstanding Actress in a Drama Series.
Since then she has had some critical success for various supporting roles in films, such as the Spike Lee film Clockers, Courage Under Fire, A Family Thing, The Negotiator, and for the telefilms Losing Isaiah and Strange Justice — a Showtime original film in which she portrayed Anita Hill — and as the lead in the PBS telefilm Cora Unashamed, based on a Langston Hughes short story. She was a cast member for all four seasons of the CBS drama The Unit as Molly Blane, the tough-minded housewife who holds the women of 'the Unit' together when their husbands are on covert assignments.
Taylor is also an accomplished stage actress, and was the first black woman to play Juliet in Romeo and Juliet on Broadway. Her other Broadway credits include Macbeth and As You Like It. She appeared in off-Broadway and regional productions of such plays as Jar The Floor, Machinal, The Illusion, A Map of the World, and The Tempest, for which she received a Dramalogue Award.