One music critic put it this way:
Few female singers matched the hard-swinging and equally hard-living Anita O'Day for sheer exuberance and talent in all areas of jazz vocals. Though three or four outshone her in pure quality of voice, her splendid improvising, wide dynamic tone, and innate sense of rhythm made her the most enjoyable singer of the age.
As an NPR profile described her, "highly rhythmic with a distinctive sense of phrasing, she was one of the first big band singers to tackle the intricacies of bebop and prevail." She was a "delightful and agile singer with a unique sense of humor," and an "original and musically literate style," who could "bend lyrics and break or stretch words" like Billie Holiday and "had a fast articulation and  deep knowledge of harmony [that] made her superior even to Ella Fitzgerald in exchanging rapid musical ideas with instrumental soloists."
Put a great documentary, Anita O'Day: The Life of a Jazz Singer, in your Netflix queue and pick up any one of her wonderful albums, especially those on the Verve label recorded in the 1950s and 1960s.
Here's a taste: Let's Fall in Love, from a 1963 date in Sweden: