Energy is a stat that allows you to do things.
Energy (Spaceship)
Your spaceship uses Energy as it travels stars and when it uses energy using tools. If your energy is drained, you can't use lasers or energy consuming tools. Also it will drain your health if you travel between stars at empty energy. You can recharge at other empires, or your colonies. You can recharge at your homeworld for free, and if your colonies it'll cost at low prices. Allied empires cost same as colonies but higher.
Captain energy
Used to activate abilities (e.g: Hop Hogs). Some tools uses energy. Read at the tools' page. If the energy is drained you'll can't use Captain parts. Your base energy is 1.000
Compact Generator: 15 energy recharged per second. Compact Battery: Increases your base energy by 500. Power Generator: 20 energy recharged per second. Power Battery: Increases your base energy by 100.
Summary
Energy is really really important. Energy is a need. This follows Health.