Beverens originated in the Belgian
town of Beveren near Antwerp
in the late 1800's. Their original color was blue and they were developed as fur rabbits, both for the texture
of their coats and the prized solid blue color
Around 1915, after the breed had been popular in England for some time, white, black and brown were developed (in all honesty meat was very scarce in England at the time because of WWI).
Modern Beverens are primarily show rabbits, but fairly rare, (you're unlikely to see one kicking around your local pet store, and if you frequent rabbit shows you're still unlikely to see a lot of these).
They weigh between 8 and 11 lbs, and have a sort of wooly coat, the fur measuring over an inch long (show rabbits are disqualified for wool shorter than 1 inch or longer than 2). The wool its self should be extremely thick and dense, silky and soft.
Beverens are primarily meat and fur producers. 'Imperfections' in their coats are taken very seriously by breeders who show them or breed them for fur. the ideal coat should be solid, bold and uniform, with no 'silvering' or white hairs disrupting it, and the ears should match the coat perfectly.
I didn't find any information about their temprament as pets, and I suspect this is partly due to their rarity.