In Castlevania: Legends there is an L meter and a B meter. The L meter is for the player's life/health, but what is the B meter for?
It's the Burning Gauge, which is related to an ability called Burning Mode that makes Sonia invulnerable to enemy attacks and doubles her attack strength:
While in this mode, she burns her "Burning Gauge" over time. It's not possible to exit burning mode until the Burning Gauge is empty. Once this gauge is depleted, she returns to normal and is not able to enter Burning Mode again. The Burning Gauge is fully replenished only when she starts a new level or a new life.
As you can see from this video (from 1'22s):