From Wikipedia: Holiday had a seminal influence on jazz and pop singing. Her vocal style, strongly inspired by jazz instrumentalists, pioneered a new way of manipulating phrasing and tempo.
Frank Sinatra had this to say about her:
With few exceptions, every major pop singer in the US during her generation has been touched in some way by her genius. It is Billie Holiday who was, and still remains, the greatest single musical influence on me. Lady Day is unquestionably the most important influence on American popular singing in the last twenty years.