Focus at the hyperfocal distance and everything from the near limit above out to infinity reads as sharp.
What focusing at the hyperfocal distance does
Most of the time a lens is focused on a single subject, sharp there and progressively softer in front of and behind it. The hyperfocal distance flips that logic for scenes with no single subject to prioritize, such as a landscape with foreground rocks and a distant ridge: focus at that one distance and everything from half of it out to infinity looks acceptably sharp in the final image, without touching the aperture again.
Why the near limit is exactly half the hyperfocal distance
The near sharpness limit sits at H/2 because of how the circle of confusion scales with distance on either side of the focus point. It is a fixed relationship, not an approximation that needs checking case by case, so once the hyperfocal distance is known the near limit follows directly without a second calculation.
Reading the aperture table
The table below holds the focal length fixed and steps through the apertures landscape photographers reach for most often, from f/4 to f/22. Closing the aperture shortens the hyperfocal distance and pulls the near limit closer, which is why stopping down is the usual way to get a wide scene entirely sharp, though very small apertures start losing overall sharpness to diffraction, so the smallest f-number is not always the best pick.
Focal length matters more than aperture
The hyperfocal distance grows with the square of the focal length, so switching from a 24mm to a 50mm lens at the same aperture pushes the hyperfocal distance roughly four times farther out, while going from f/8 to f/16 only halves it. A wide lens set to a moderate aperture reaches a short, practical hyperfocal distance far more easily than a long lens does, which is one reason wide-angle lenses dominate landscape work built around this technique.