Henry Jennings was born in Cope, South Carolina, the son of Henry C. and Florrie Tatum Jennings. He received an A.B. degree from Clemson University and an LL.B. from the University of South Carolina. He was admitted to the Bar in 1917 and commenced practicing law with his uncle, Thomas H. Tatum, in Bishopville in 1919, and later with his two sons, Jacob and Robert.
In 1925, he married Mary Green Hill and they had three sons, Henry Caldwell, Jacob Hill and Robert Dennis, who survived him. He served in the South Carolina Legislature in 1923–24 and again in 1950. He served as a Special Circuit Judge and sat as a Special Associate Justice of the South Carolina Supreme Court.
He served as President of the Lee County Bar Association, Chairman of the Lee County Democratic Party for over 20 years, a charter member and first President of the Lee County Kiwanis Club, Commander of the American Legion, Chairman of the Lee County Board of Education, organizer and President of Home Federal Savings and Loan of Bishopville, and was active in the Pee Dee area Boy Scouts of America.
A lifelong member of the Methodist Church, he served as a Sunday School teacher, Superintendent of the Church School, Chairman of the Official Board and an honorary life member of the Board of Trustees of the Bethlehem United Methodist Church. He was a member for over sixty years.