Griffith was born in Seguin, Texas, and her career has spanned a variety of musical genres, predominantly country, folk, and what she terms "folkabilly." Griffith won a Grammy Award for Best Contemporary Folk Album in 1994 for her recording, Other Voices, Other Rooms.

This album features Griffith covering the songs of artists who were her major influences. One of her better-known songs is "From a Distance," which was written and composed by Julie Gold, although Bette Midler's version achieved greater commercial success. Similarly, other artists have occasionally achieved greater success than Griffith herself with songs that she wrote or co-wrote. For example, Kathy Mattea had a country music top five hit with a 1986 cover of Griffith's "Love at the Five and Dime" and Suzy Bogguss had one of her largest hits with Griffith's and Tom Russell's "Outbound Plane".

In 1994, Griffith teamed up with Jimmy Webb to contribute the song "If These Old Walls Could Speak" to the AIDS benefit album Red Hot + Country  produced by the Red Hot Organization. Griffith was a survivor of breast cancer which was diagnosed in 1996, and thyroid cancer in 1998.