Energy is what enables your spartan to perform certain actions, such as attacking, reviving, and busting other players out of jail.
Energy recharges faster for Deluxe accounts that it does for free accounts.
Your energy bar can be refilled by paying with gems at the gem temple (Explore>base exchange>gem temple).
Your energy can also be refilled with Energy Refills or Energy Shots
A more in-depth way of getting large amounts of energy is bounty hunting.
Attacking someone uses 50% energy.
Busting uses 10% energy.
Reviving uses 50% energy.