Energy is used to collect Materials or Simoleons from buildings, doing quests etc. It is recharged over time; 3 minutes per Energy. You can get more by waiting for it to regenerates, visiting friends, asking friends, random bonus energy by collecting materials/simoleons from building, levelling up and buying energy deal with diamonds.
There are also now several power plants factories available in the game from which you can collect Energy. Such as the Coal Power Plant gives you 5 Energy. (Get power plant from middle and right deal in Spin City ONLY). Solar Power Factory DOESN'T make any energy!
The Energy gauge is located below the Experience gauge. It will show how much energy you have. If it's below 5 energy, it will show a text "Get More". If you run out of energy It will show a popup "Out of Energy!" with a box and a purchase package.
You can also open the Inventory and click at the energy tab to use.