She graduated from Lincoln High School. She remained in north Florida for college and graduated from Florida A&M University (then known as Florida A&M College for Negroes) in 1946. At this time, African Americans could not attend graduate school in Florida, so Meek enrolled in the University of Michigan and received her M.S. degree in 1948.
She served in the United States House of Representatives from 1993 to 2003, representing Florida's 17th congressional district. After graduation, Meek was hired as a teacher at Bethune-Cookman University in Daytona Beach, Florida, and then at her alma mater, Florida A&M University. Meek moved to Miami in 1961 to serve as special assistant to the vice president of Miami-Dade Community College.
The college was desegregated in 1963, largely due to Meek's integral role in the push for its integration. Throughout her years as an educator, Meek was also active in community projects in the Miami area. Meek was elected to the Florida House of Representatives in 1978 as a Democrat, serving until 1983.
As a state representative, she introduced a bill criminalizing stalking. In 1982, she was the first African American woman elected to the Florida State Senate. As a State Senator, Meek served on the Education Appropriations Subcommittee.
Her efforts in the Legislature also led to the construction of thousands of affordable rental housing units. Meek was elected to the U.S. House of Representatives in 1992, after fourteen years in the Florida Legislature. This made her the first black lawmaker elected to represent Florida in Congress since Reconstruction.
Upon taking office, Meek faced the task of helping her district recover from Hurricane Andrew's devastation. Her efforts helped to provide $100 million in federal assistance to rebuild Miami-Dade County (then known as Dade County). Also while in the House, Meek successfully focused her attention on issues such as economic development, health care, education and housing.
She led legislation through Congress to improve Miami-Dade County's transit system, airport and seaport. Construct a new family and childcare center in North Dade County. And fund advanced aviation training programs at Miami-Dade Community College.
Meek emerged as a strong advocate for Haitian immigrants and senior citizens. Meek claimed that her district — Florida's 17th Congressional district — was undercounted in the 1990 Census. She believed that her constituents were cheated in the 2000 Presidential Election.
Meek refused to attend a meeting with President George W. Bush in February 2001.
Meek was a member of the powerful House Appropriations Committee, in addition to serving on the Subcommittee on Treasury, Postal Service and General Government and the Subcommittee on VA, HUD, and Independent Agencies. She is a member of Delta Sigma Theta sorority.