a guess

"Right of common" basically means that there is the "right" for the land (common) to be used in common. (Please see partial definition below).

http://en.wikipedia.org/wiki/Common_land

Commons rights

Historically most "rights of common were appurtenant[2] to particular plots of land, and the co"mmoner would be the person who, for the time being, was the occupier of a particular plot of land (or in the case of turbary, even a particular heath). Some rights of common were said to be in gross, that is, they were unconnected with ownership or tenure of land. This was more usual in regions where commons are more extensive, such as in Northern England or the Fens, but also included many village greens across England and Wales. Most land with appurtenant commons rights is adjacent to the common or even surrounded by it, but in a few cases it may be some considerable distance away.


Modern-day pannage, or common of mast, in the New Forest
Example rights of common are:
Pasture. Right to pasture cattle, horses, sheep or other animals on the common land. The most widespread right.
Piscary. Right to fish.
Turbary. Right to take sods of turf for fuel.
Common of marl. Right to take sand and gravel.
Mast or pannage. Right to turn out pigs for a period in autumn to eat mast (acorns and other nuts).
Estovers. Right to take sufficient wood for the commoner's house or holding; usually limited to smaller trees, bushes (such as gorse) and fallen branches.[3][4]
On most commons, rights of pasture and pannage for each commoner are tightly defined by number and type of animal. For example the occupier of a particular cottage might be allowed to graze fifteen cattle, four horses, ponies or donkeys, and fifty geese — the numbers allowed for their neighbours would probably be different. On some commons (such as the New Forest and adjoining commons), the rights are not limited by number, and instead a marking fee is paid each year for each animal turned out.[5]

- Also, the below website may be of interest to you:
http://data.lullar.com/入会権


http://www.kikori.org/yogo/yogo-shu3.html
旧慣使用林野
2009/07/05更新　
読み： きゅうかんしようりんや
説明文： 旧慣使用権とは、地方自治法の規定により、当該市町村の住民が、旧来の慣例に基づいて市町村又は財産区の所有する公有財産を使用する権利である。

旧慣使用林野とは、この権利に基づき主として、木竹の育成又は採草、放牧に利用される土地をいう
旧慣 = 旧来の慣例