The hyperfocal distance is, as stated above, the closest distace at which you can focus where infinity will fall within the acceptable DoF range. When focused at the hyperfocal distance, the close limit of the acceptable DoF will be approximately one-half the hyperfocal distance (actually one-half the hyperfocal distance less one focal length).
Knowing the hyperfocal distance is useful for several purposes, such as tracking moving objects in the near distance without constantly refocusing, or taking quick pictures without having to focus first.
This latter use, taking quick pictures, is the concept behind "fixed-focus" point and shoot cameras. If you were designing a camera for general use, where the camera has a fixed-aperture, fixed-focus lens (à la the old Kodak Brownie), you would set the focus point of the lens at the hyperfocal distance to make the camera as general-purpose as possible.
In the old days before autofocus, many photographers would keep their SLRs set to f/8 and the focus set to the hyperfocal distance, with the shutter speed set for the proper exposure with the film being used. This was called "Brownie-ing" the camera. The camera was then ready to take an instant picture upon demand.
Many famous photographs were taken this way. Such pictures were rarely photographically perfect, but many won their takers much money and/or fame, such as the image of the flaming passenger jet nose-diving at full power into the North Park area of San Diego.
This technique was so common that most lenses had the DoF for various apertures right on the lens. Setting the lens at the hyperfocal distance was a no-brainer requiring zero calculations.
In today's photographic environment, this technique is not nearly so useful for several reasons.
First, autofocus has improved to the point where it is almost instantaneous with a good camera and a good lens. This makes it unnecessary to preset a camera in order to obtain good virtually instantaneous pictures.
Second, the proliferation of zoom lenses has rendered hyperfocal distances difficult to calculate in the field. For a given aperture, a zoom lens has an infinite number of hyperfocal distance between the minimum and maximum foxal lengths.
And third, even good prime lenses typically no longer have DoF scales, requiring in-field calculations (or good memorization).
Hyperfocal shooting has become somewhat of a lost art for general photography.