A reason energy can be difficult to understand is that it is not a natural unit of measure. Energy is a derived concept. It can be derived from the fundamental units of mass, length, time, charge and temperature, but it is not a base measure in itself.
The reason energy definitions contain the concept of "doing" something, such as the ability to do work, is because that's what the human concept of energy is.
There are two ways I can try to explain energy, the top-down approach and a bottom-up approach. I'll use the bottom-up here.
The concept of energy arises from the four fundamental forces in nature.
We know there are four fundamental forces in nature: gravity, electro-magnetism, and the strong and weak nuclear force. There are 3 things that can occur resulting in a difference in force. 1. The force can change strength over a spacial distance. 2. At any particular point in space, the force can change strength with respect to time. 3. Two or more forces can be present on the same point in space.
If you've had calculus, you'll recognize quickly that energy is just the derivative of force strength with respect to position, time, another force, or even all three. For those who haven't had calculus, energy is the rate of change of force strength when position, time, or the strength of another force remain constant.
So energy is a consequence of changing force strengths. It isn't something that exists by itself. That's why it's a concept and can be difficult to understand.
Is energy the motion of particles? In most cases yes, the interactions of forces with time, distance, and each other generally cause energy to be seen in the form of particle movement or vibration. Not in all cases though. Electric charge and electron spin are two examples. (Spin is a misnomer because it doesn't mean an electron spinning on an axis at all.)
There are generally two ways energy is quantified. The first is a measure in comparison to the surroundings or environment. The second is in comparison to some ground state where no forces are present.