A B battery is any battery used to provide the plate voltage of a vacuum tube. It is sometimes colloquially referred to as a "dry battery" (although there's no reason why a "wet" battery of suitable voltage couldn't be utilised for the purpose).
The filament is primarily a heat source and therefore the A battery supplies significant current and rapidly discharges. The B battery experiences comparatively little current draw and retains its stored capacity far longer than an A battery. Early B batteries used with bright emitter tubes were 120 volts, but these quickly became obsolete as they were replaced with examples having voltages of typically 45 volts, 67½ volts, or 90 volts as more efficient tubes became available. Some examples had taps every 22½ volts.
Even when the plate voltage rail is fed by a power supply rather than a battery, it is generally referred to as the "B+" line in American schematics.
Because plate voltages can be as high as 300V DC, multiple B batteries may be connected together in series to additively provide the required operating voltages. The much higher available voltage of B batteries means that they must be handled more carefully than other battery types due to their ability to shock and/or burn the person handling them.
In Britain and in some other countries, the "B" battery was known as the "HT" (high tension) battery.
Read more about this topic: Battery (vacuum Tube)