Billie Holiday was one of the greatest and most influential jazz singers of the 20th century. With a voice as delicate as the gardenias she would often wear in her hair, Holiday forged a new style that was inspired, partly, by the horn playing of Louis Armstrong. As the New Grove Dictionary of Jazz says:
More than nearly any other singer, Holiday phrased her performances in the manner of a jazz instrumental soloist, and accordingly she has to be seen as a complete jazz musician and not merely a singer. Nevertheless, her voice, even in the light and lively numbers she often sang during her early period, carried a wounded poignancy that was part of her attraction for general audiences. Although Holiday claimed also to have taken Bessie Smith as her model, she sang few blues, and none in the powerful, weighted manner of Smith. She was, however, a master of blues singing, as for example on Fine and Mellow (1939), which she built around blue thirds descending to seconds to create an endless tension perfectly suited to the forlorn text.
You can hear Holiday perform "Fine and Mellow" and other great songs in this 2009 documentary called Billie Holiday--The Life and Artistry of Lady Day. The film is only 28 minutes long, so don't expect a nuanced telling of Holiday's troubled but extraordinary life. Indeed, as one reviewer rightly says, it offers "the shallow insight of a Wikipedia article." What makes this low-budget documentary worthwhile is the music. The film features some of the best surviving footage of Holiday performing, including scenes from Duke Ellington's 1935 Symphony in Black, the 1947 film New Orleans, and the CBS broadcast "The Sound of Jazz," which was recorded in 1957, only two years before Holiday's untimely death at the age of 44.