Most new jazz singers are all excited about improvisation (rightly so) but they think the most important part of improvisation revolves around pitches. Nope! The single most important thing in jazz is rhythm and groove. You can sing all sorts of crazy notes and it won't sound like jazz if you can't groove.
So what is “groove?” Our friends at Wikipedia describe “groove” as the sense of an effect ("feel") of changing pattern in a propulsive rhythm or sense of "swing". In jazz, this comes down to syncopation. Rather than give you a long theoretical explanation, let's discover what this means by listening to a really great jazz singer. Since my sample lead sheet was “All of Me,” let's keeps using that song as an example. Here's a clean version without all of my annotations.
To do this exercise, you need to find Ella Fitzgerald's version of “All of Me” on a streaming service or YouTube. Listen to Ella's version while you read along with the lead sheet. Pay particular attention to what she's doing rhythmically. Is she following the rhythms as they are written? If not, what is she doing? Can you find a pattern?
If you noticed that she's singing off the beat a lot of the time, you're right on. Most of her phrases begin off the beat and on the beat. On top of that, she often puts a little bit of stress on off-beat notes. For another great example of swing feel, listen to “Splanky” on the Basie band's album titled The Atomic Mr. Basie. Tap your thigh lightly with your hand on the beats while you listen. Note how much attention is paid to off beat rhythms. You will definitely hear and hopefully feel the power of swing rhythms. While you're at it, listen to the whole album – it's one of the swingingest (a new word?) albums of all time.
Homework – Take the medium swing tune that you chose from my 100 Standards for Singers list on the Resources page. Sing the song while you lightly tap your hands together. Try beginning each phrase ½ beat early. This is called “anticipation.” Then try singing the song while singing each phrase ½ beat late. This is called “back-phrasing.” Finally, try ending every phrase off the beat while using either anticipation or back-phrasing on the beginning of every phrase. This can be quite challenging for some people, so feel free to sing at a fairly slow tempo like 90 BPM.