I have to admit, it took me a few seconds of disorientation before suddenly the picture geometry snapped into my brain. It was like one of those optical illusions where once you see it, you can't not see it!
So what's going on here? Actually, a lot! So strap yourself in.
Basically, Cassini was behind Saturn when it took this picture; the sun, Saturn, and Cassini were almost exactly all on a straight line (for pedants, the Sun-Saturn-Cassini angle was 178°). From Cassini's point of view, Saturn was almost completely unilluminated by the Sun. In others words it was over the night side of the planet.
The Sun is shining down on the rings a bit, and Cassini is viewing them from underneath. Off to the right, you're seeing the rings with sunlight scattering through them. The dark triangle is Saturn's shadow on the rings. The curved line of the triangle on the left is the limb of the planet.
So what's with the rings on the left? Is that the shadow of them on Saturn? Nope, it can't be, because the Sun wasn't lighting them up. So those must be the rings themselves in silhouette! The lit-up part of the rings on the right reflect light onto the dark side of Saturn, illuminating it a little bit. That's why you can see the disk of the planet at all. But the rings go all the way around, and on the upper left, they block that small amount of light coming from the planet.
OK, fine, then what's that weird faint glow on the planet then just below the silhouetted rings? Ah, that's light scattered from Saturn's own atmosphere! After the Sun sets on Earth, the sky is still lit up a bit, right? It's only when the Sun is well and truly set, about 90 minutes later, that it gets completely dark. That's because sunlight hits the Earth's air and bounces around, letting it light up the air a bit on the dark side of the Earth.
Same thing here on Saturn: that glow is a little bit of sunlight that got scattered by air closer to the lit side of the planet, and it gives the dark side a taste of light. I guess you could say that if you were floating in Saturn's atmosphere, at that point, it would be twilight for you. And if you looked up, you'd see the magnificent rings coming across the sky, then suddenly cut off by Saturn's shadow. What a sight that would be!
Still having a hard time? This may help. Remember this glorious picture of Saturn from 2006?
This is a mosaic of quite a few images, stitched together to produce this magnificent portrait. The Sun is behind the disk of Saturn, and you can see the rings lit up on the sides, but in silhouette against the disk itself.
Now imagine the shadow of Saturn is cutting off a piece of the rings:
I Photoshopped in the shadow (I know, the angle is all wrong, but this is supposed to be illustrative, not perfect), and then put a red box around the region showing, more or less, where the new image is (I also flipped the original full-Saturn image around so that it better matches the new image). Now do you get it? We see the lit rings on the right, the shadow of Saturn across the middle, and the silhouetted rings against the disk of the planet! Mind you, this isn't an exact match, and what I did was very crude and not terribly accurate, but I hope it's more -- wait for it, wait for it -- illuminating.
Very cool. I remember when the Voyager probes passed Saturn back in the early 80s. The pictures were incredible! We learned a lot, and it inspired a generation of would-be astronomers (including me). But those spacecraft flew by Saturn at high speed. Now we have Cassini orbiting Saturn, as it has so many times since 2004, and with that residence comes views like this. It's what happens when you plan to stick around a while.