The basic concept is that it is the space between the notes that counts.
I’ll try a practical example first.
In the past, when I have played with rock bands that covered Led Zeppelin tunes, I was often asked “How did you make yourself sound so much like John Bonham?” I wasn’t using a kit even close to what he had, the sound was completely different, and yet I was able to emulate his style. The reason is that Bonham played his upbeats “behind the beat” while his downbeats were sometimes just a tad “ahead of the beat”. The result was that when Bonham played a straight eighth note feel, it had swing to it. The swing came because of the proportion of time between the downbeats and the upbeats. He was keeping a very “laid back” feel.
Conversely, when I have played in Jazz bands (and to an extent fusion ensembles), I play all notes slightly “ahead” of the beat (while keeping a swing proportion). The reason is that in jazz, the drummer is “driving” the band where as in rock; the drummer is holding the band back a bit.
Now, when I was younger, I used to think of a beat as being a long line (much like a note on a midi piano roll). But when I went to Berklee, I found that the idea of a circle is better. The reason is that there are far more points on a circle. The trick is to be able to manipulate this circle consistently. Many drummers are right on the beat (Early Rush) which sounds mechanical. Some drummers are all over the circle (No uniqueness). One who has command of the circle has a very identifiable sound and a superior feel.
This is not limited to drummers however. This applies to all instruments. Two sax players can play the same jazz solo, but the one that commands the circle is going to be the smokin’ player. They may not even know about the circle – it just comes naturally, yet that is what it is.
If you were to watch me play, you would see that when I hit the snare drum, I am not hitting it straight down. The motion is more like a crescent. I am simply completing the circle.
Hope this helps a little. It is difficult to explain.