As used in these stories:
Also known as prana or chi, energy is the vital spirit that resides within all that draws breath and lives, binding individual entities together as parts of a unifying whole.
With practice, most people can learn to perceive energy, some more strongly than others.
Most energy tends to be perceived via a physical sense, but the sense and ability to discern it varies from person to person. Some people feel something like heat or tingling in their skin; others are more visual, identifying the energetic perception through the words of color, shape, visions or sharpness. Some hear, taste or smell something unique, which others do not.
Regardless of how an individual perceives energy, it exists, and the lack of it in an individual entity means what they were is no longer connected to the vast scape of life as we know it.