Private Brands (PB) are brands owned by retailers and not producers. Most well known brands are owned by food producers and are called National Brands (NB). In recent years, the use of PB has exploded as retailers flex their muscles and as a way of keeping product prices down.
This is not a welcome development for food producers because they depend on brand value to keep prices high enough to make profits. With PB, the retailer simply defines the product specifications and then lets producers bid the rights to produce the product. This reduces the food producers to not much more than contract manufacturers. The up side for producers is that such contracts are usually for large volumes.
One example of PB which is not new is the milk you see at McDonald's. If you look on the side, it is manufactured by Meiji Dairies. Newer examples are convenience stores which are increasing the number of PB very rapidly. Seven-Eleven is part of Seven and I Holdings, therefore both Seven-Eleven and Itoyokado both sell the same PB products. It appears to me that this is an attempt to replace NB, because the prices do not appear to be greatly discounted. I suppose this is why the line is called "Seven Premium".
In an article on Nikkei Trendy, the way Lawson is using PB to keep prices down, as well as the the moves by both Lawson and Seven and I Holdings to make a wider variety of more basic items such as seasonings as PB.