Energy is one of two resources in Supreme Commander; the other is mass. Energy is required to build structures and units; it is also drained to maintain stealth/cloaking fields and shields, fire artillery structures and other things.
Energy is produced by power generators or the resource allocation system implemented in ACUs and SCUs.
Importance
In Supreme Commander, energy is not especially difficult to get by, and is usually not the limiting resource. If you need energy, all you have to do is build power generators, and that is all. However, running out of power can have devastating consequences. All of your intel structures will go offline, not only leaving you in the dark, but losing the units you identified in the past too. Your shields will deactivate, leaving your base vulnerable, but also your shield generators and your shielded units especially vulnerable (they have very low HP, usually). Your mass extractors will also cease to function, lowering your mass income. Finally, getting out of this situation is especially difficult, as power generators mainly cost energy to produce, the resource you currently don't have. As much as you can, try to never run out of power.
See also
For information about the second resource in Supreme Commander, mass, visit the mass page.