It's an almost mystical term used by farriers. Establishing it is perhaps the most essential aspect of the horseshoer's art. Many horse owners don't fully understand what hoof balance is. But they know that if their horses don't have it, they may suffer from poor movement, interference, or lameness. Many good farriers don't seem to consciously know the technical features of hoof balance, but instead have developed a subconscious understanding of it through years of experience.
Hoof balance is four dimensional geometry.
The fourth dimension is Time, which manifests as movement, growth, and change. It's this fourth dimension that makes things tricky. The most commonly measured aspect of hoof balance is toe angle. Somewhere along the line, long before the hoof protractor was invented, some fellow who probably never shod horses decided that 45 degrees was the proper toe angle for front hooves. This erroneous idea has been passed down in books from around 1800 to the present.