In my experience, the subject of energy tends to be badly taught in lower-level physics classes. I’ve met a lot of students who, when asked what energy is, can promptly recite the following answer: “Energy is the ability of a system to do work.” Continuing with this website’s theme of trying it yourself, I recommend that you take a field trip to the nearest university campus or high school science class and perform this very experiment, and watch the pride in the students’ eyes as they prove their intelligence to you.
But if you want to throw a bit of a wrench into things, try following up your first question with another: what is work? Many students will frown slightly. Some will say that it is a force exerted over a distance. Others will simply shrug and point at the formula. In other words, most physics students don’t really understand what energy is.