Actually I thought that ST1100 gave a very good explanation. Just think a bit about what he said. This is my understanding of it:
Let's say we draw an infinitely small black dot (or, in real terms, say 0.001mm diameter) on a white piece of paper, and try to focus that image on your camera. When the image of that black dot is out of focus, it appears like a grey circle. As you gradually bring it into focus, it becomes smaller and smaller as it approaches the size of the black dot. The circle of confusion is the size of that black dot on the film when it is CONSIDERED to be in focus ie when your eye can't tell the difference even if it becomes more sharply focused after that. In the case of 35mm film, this is usually ARBITRARILY determined to be 0.03mm diameter. In other words, even if you manage to focus until that dot is 0.01mm diameter on your film, it won't APPEAR any sharper.
For a DSLR, because of the crop factor, the focused image of that dot should be smaller (eg 0.02mm) ie the circle of confusion should be tighter. This is because the DSLR sensor is smaller (0.6X crop factor). If you blow up both the 35mm film image and the DSLR sensor image to, say, 8R size, the DSLR sensor image will be more highly magnified. That 0.03mm dot will be magnified MORE than the 0.03mm dot on the film negative. If the image is considered in focus when the circle of confusion is 0.03 for a DSLR image, then the DSLR image will appear less sharp. In other words, there needs to be a tighter tolerance for focusing with a DSLR, to achieve the same degree of sharpness for any particular print size.
The DOF scale on a 35mm SLR lens indicates which area will be considered "in focus" ACCORDING TO 35MM FILM FORMAT, ie the circle of confusion is arbitrarily taken to be 0.03mm in calculating the DOF achieved at any particular aperture. This is a looser tolerance than a DSLR requires, and therefore may not be accurate for a DSLR. Why are we talking about a DOF scale? Because the original question was about hyperfocal focussing, which presumes the use of a DOF scale.
In PRACTICE, I doubt that the difference matters very much at all. Just use the old rule of thumb: f8 and be there. If you want to be a bit more kiasu, use f11. But it better be very bright, or you better be using a tripod.