Others here will be able to explain Hyperfocal distance better than I, but here goes...
It is when the depth of field for a lens at a certain aperture is more or less from near to infinity.
When you focus on something such as a sign across a street a certain percentage of the foreground and back ground will also have acceptable sharpness. As you stop down those percentages will increase. At some point everything near to infinity will have the same degree of sharpness. Unfortunately, as you stop down the light begins diffract and the image begins to lose overall sharpness. This is why it is recommended to not stop down beyond f32.
As an example when I use my Mamiya 50mm at f/8 and focus about 15-20 feet out everything from about 5 feet to (maybe) 60 to 80 feet is in focus. The area behind the point of focus is always larger than the area infront. If i stopdown to f/11 I get just about everything from a couple feet to infinity in "focus." This would be the hyperfocal distance for that lens at that aperture.
There is a great little windows application that can figure depth of field for any lens length, aperture and film size. I used to have it installed, but can't find, nor do I remember its name. Maybe someone out there knows and will post the url.
Meanwhile, If you are using swings and tilts to change the focal plane you can get more in focus (assuming it is in the plane of focus) with a larger aperture (smaller f number). This allows you to avoid the problems of stopping down too much. THe problem with this a approach is two fold. 1. if you have to adjust the rear standard it will distort the subject. 2. If and when something falls out of the plane of focus it falls out fast and can look very strange. The other problem with this type of focusing is it often requires a lens with a big image circle. There is a strange, unpronounceable name for this type of focusing -- which I have never tried to remember.
I hope this helps.