Wikipedia (it's not the authority in everything -- I know -- but it's convenient) says:
Kvass (literally "leaven"; borrowed in the 16th century from Russian квас), sometimes translated into English as bread drink, is a fermented mildly alcoholic beverage made from black or rye bread.
Of course, just as there are non-alcoholic "near beers" and Coca-Cola doesn't contain cocaine anymore, there may be varieties of kvass with no alcoholic content.
The beverage enjoyed by Muscovites, other city dwellers and villagers throughout Russia is kvass, a lacto-fermented beverage made from stale rye bread. It tastes like beer but is not alcoholic.