The Energy Gauge is a feature that appears exclusively in A Link Between Worlds.
The Energy Gauge functions similarly to the Magic Meter and the Stamina Gauge from Skyward Sword. Link obtains the Energy Gauge after Ravio gives him the Bow for the first time. The Energy Gauge depletes whenever Link uses an item from the shop, or when he merges on to a wall.
Once the Energy Gauge is completely depleted, Link is no longer able to use Ravio's items or use his merge ability until the Gauge is replenished. The Gauge can be replenished naturally over time or by the use of an Energy Potion.