"Hyperfocal" refers to the condition where depth of field allows the lens to be "in focus" from some minimum distance to infinity.
This depends on a core assumption: the size of the acceptable "circle of confusion," which is determined by the actual aperture diameter and lens focal length, but also by the amount of enlargement the image will receive before final viewing. That is, a 250 mm lens at f/11 will have greater depth of field on an 8x10 negative than it will on an APS-C or Micro 4/3 digital sensor, because the 8x10 is likely to be viewed as a contact print, while the crope sensor image will be enlarged at least to screen viewing size (around 20:1, give or take).
Once this acceptable circle of confusion is determined, it's a fairly simple calculation to determine how far in front of or behind the plane of critical focus objects can be and still produce images with this size or smaller circles of confusion. This takes the form of a table or graph that is condensed into a depth of field marking on a lens or focusing rack.
Finally, one can then set a focus that, at the specified aperture setting, will produced "in focus" depth of field that just extends to infinity, and generally to half the set focus distance (many old box cameras were actually focused at about 10 feet, but had aperture that made them hyperfocal, so they'd say "five feet to infinity" or "place your subject at least five feet from the camera").
It's important to remember that "depth of field" isn't a physical condition or quality -- it's a measure of how much defocus the user is willing to accept. If you scan an 8x10 negative that looks razor sharp all over to the eye at high enough resolution and examine it at 1:1 on a good monitor, you'll find that even at f/32 there's still a plane of critical focus, and everything not in that plane is at least a little bit fuzzy -- but if the fuzziness isn't visible in normal viewing, we consider that "within depth of field," and if that depth of field extends just to infinity, the setup was hyperfocal.