For some reason, this perfectly legitimate question seems to spawn far more than its share of bad threads. So what is energy and how do conversations about what it is go wrong?
Energy in Newtonian mechanics
The first definition of energy that is usually encountered is “energy is the capacity of a system to do work”. Work is then defined as a force applied over a distance. When an object with some speed collides with another object it can exert a force on that other object and move it some distance. So a moving object has “the capacity to do work” which is energy, specifically called kinetic energy.
From the laws of Newtonian mechanics and these definitions it is possible to derive the work-energy theorem. This theorem basically says that for a rigid object the net work done is equal to the change in kinetic energy. Similarly, it is possible to derive other forms of energy, such as gravitational potential energy or elastic potential energy, and to show how those forms of energy can be converted to other forms or transferred from one system to another through work.
Energy in other contexts
There are other definitions of energy which are used in thermodynamics, Lagrangian mechanics, and quantum mechanics. There are also proofs that demonstrate how energy in one context is related to energy in the other contexts. Those other definitions are also often brought up in a discussion about What Is Energy, and many people have a preferred definition. For simplicity, we will stick with the usual first textbook definition, in no way implying that it is preferable to any other definition. The discussion below applies for all the other definitions as well.
How the conversation goes wrong
The first way that conversations about energy go wrong is that, when someone provides a definition, the questioner essentially says “No, it cannot be that easy, what is energy REALLY”.
It is that easy. Energy is a defined quantity, and the definition tells you what it is. It doesn’t matter if you ask “What is energy” or “What is energy really truly actually” the answer is the same: the definition. For any word, X, the answer to “what is X” is the definition of X, and this includes energy. Energy is simply a defined quantity, defined as above. The reason that we are interested in energy is not that the definition is tricky or involves any hidden magic, but that it is useful. It is useful because it is conserved and it is related to other useful quantities.
The second way that conversations about energy go wrong is when questioners have the impression that energy is some type of “stuff” that has its own independent existence and they seek to find out what material the “stuff” of energy is made of. In some ways, this impression is well founded. After all, energy is conserved and it can be moved from one system to another, just like you would expect from your everyday experience with “stuff”.
Energy is not a thing with independent existence. It is just a defined quantity used to describe a system. This is similar to mass, charge, momentum, and any other similar defined quantity that we use in physics. Just like you cannot have “pure mass” independent of a system which “has” the mass, the same thing holds with energy. Sometimes questioners mistakenly think of light (photons) as being “pure energy”, but light has momentum and other properties also.
The third way that conversations about energy go wrong is when a poster knows and understands the definition of energy (either the “capacity to do work” definition or one of the others not covered here), but refuses to accept it for some reason.
There is not much to say about this one. We use definitions so that we can understand each other. If someone refuses to use the same definition as other people, then confusion results. In physics (as in the rest of life), often the same word is used with subtly different meanings in different contexts. It is important to be familiar with the various different definitions when you are dealing with the different contexts mentioned above. It certainly is not a problem to have a favorite definition and to explain why it is your favorite, but recognize that the other definitions have their place also.