I can relate to your confusion on this, because wrapping your head around what energy is takes a little time. Energy is not just one thing with some basic fundamental form.
The definition "the ability to do work" really does define and bind together all the different forms that energy takes, so let's look at "work" closer.
Work = force * distance(I'm sure this is familiar to you)
Breaking it further,
force = acceleration * mass
So, work = acceleration * mass * distance
Essentially, work occurs anytime mass is accelerated over some distance. So, energy is anything that gets mass to move.
I'm sure you can think of a multitude of ways to move mass around.
Ex 1. Electromagnetic radiation from the sun striking atoms in your head, causing them to accelerate and move around more quickly (at the atomic level "heat energy" is the number and velocity of atoms & molecules. A substance is hotter if its atoms are zipping around faster.)
Ex 2. Gravity causes mass to accelerate towards other mass (if there is motion -- like a mountain collapsing in a landslide -- it is kinetic energy). (if there is just the possibility of motion -- like a mountain that hasn't fallen down yet -- it is potential energy).
Ex 3. Chemical energy -- as chemical bonds form, they release electromagnetic energy, which can strike other atoms and get them to move faster ... back to Ex 1. ... they get "hotter."
Ex 4. A wrecking ball smashes into a building and causes all the bricks in the wall to move, so it has given them energy (and since the wrecking ball decelerates during this process, it loses energy)
So again, the basic idea is that energy is not one thing. It really is anything that can get mass to move around. See the following for more details and explanation: http://www.energyquest.ca.gov/story/
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