The previous answers are more than adequate expressions of the idea of 'energy' as a tool in physics--but I think you are asking more than that. You may wish to investigate the original proposition of 'vis viva' or 'living force' by Leibniz. What you will often hear in such discussions of 'energy', as was said here, is that physics or physicists cannot say ultimately what 'energy' is, and are constrained to this practical application of the very idea of energy to the notion of its conservation, which while it may in general be true (that a measurable quantity of energy functions as a parameter of continuous symmetry), can say no more about it.
However, this view is not necessarily correct, that it is somehow impossible to say what energy truly is; on the contrary, it is only the approach of physics which impedes if not prohibits the consideration and resolution of that question, and many others. And you are quite intuitively correct to suppose that energy may eventually be defined at least as the function of a more fundamental relation.
Energy is ubiquitous in reality, and as we are told in QFT, even the vacua of its quantum fields are continuously energetic: viz. there is no state which can realistically be said to be without energy. How then can we explain this; and if indeed energy is a function of motion, what ultimately is moving? One is entitled to ask then, since energy is classically and in any real context only the motion of a force over a spatial distance--i.e. the spatial integration of the force--, what force may be conceived to act ubiquitously in this way to imply ubiquitous energy? And it is reasonable to say that orthodox physics is effectively stalled at an impasse between the perspectives on this question embodied in QFT and GRT, essentially because it prohibits itself from formulating precisely and explicitly such a question; the arcane musings of M-theory notwithstanding.
In order to address such a question however, what is required--and what the sciences have come to regard as anathema-- is first simply to propose a priori the existence of a unitary universal substance or fabric, and to understand that because we too are comprised of it, not only is it impossible to discern its ultimate nature, but that due to this very constraint, its essence becomes effectively equivalent to the ubiquitous force holding the universal unity and entirety together. All of reality then is effectively only the dynamic action of this singular force in various contexts of its more-or-less local distribution; and one proceeds to consider how it is that the existence of such a force acting everywhere at once permits the world of matter and space, perpetually inflated, as we perceive it.
At the same time, there is no need to dispense with the magnificent theories of QED and the mathematical methods perfected in the structure of the SM; for it is only the more fundamental physical basis of these theories which we seek, and which, if a viable model of such a foundation is indeed revealed by the correct pursuit of the reasoning suggested, is quite amenable to the same rigorous calculus.
To reiterate then, were one to suppose that the universe is composed entirely and exclusively of a singular inviolate substance, it would be quite impossible for us, also comprised of it, to determine its ultimate nature. Since however we are embroiled in its dynamics, we are therefore capable of, if also constrained to, an understanding of its principles --operating continuously all around and within--, commencing with some meditation on the self-evident postulate, more properly an innate perception, that a unitary force must bind that inviolate universal unity or substance together.
That is, as the ancients understood it, the universal entirety, in whatever it eventually consists, must by very definition hold itself together; so that with this self-evident knowledge, a priori, one is first required to inquire how it is able to do this without collapsing upon itself; to which the answer is that, since this 'cohesive effect' is universal and must operate at or through every conceivable spatial point, that force of 'cohesion' must be acting in disparate components at any and all such points; the holding together one way tends to balance approximately the holding together in the opposite direction at any point. When imagined with respect to a common archetype--say the purely geometrically-defined interval on a universal cubic lattice (comprising infinite mutually 'cohesive loci' in perfect equilibrium)--, these disparate or asymmetrical components of a 'cohesive force' are effectively vibratory in origin and in reality always slightly out of phase with each other within a range defined by half that interval; and any 'field theory' attempting to describe these vectors of cohesive force and their relations is of necessity bound fundamentally by constraints of such a 'phase relation'.
What results from this interaction between points defined by disparate resultants in such a 'cohesive force' then is a ceaseless motion as these components (arising eventually from the interior dimension of 'spatial depth' itself) act one against the other throughout universal reality in an inherent tendency to (impossible) equilibrium or 'cohesive symmetry'. That motion we call 'energy', whether in the relative vacuum of space or in the midst of what we describe as 'matter' by virtue of our similitude with it, and consequently our capacity to perceive some condition of resonance with it (within a definitive range); and the distribution of that 'cohesive force', of which all ostensible forces are aspects, constitutes the properties of reality, mass, charge, momentum, and energy when that is understood as an oscillatory principle in that distribution. The reciprocal cubic lattice model of 'cohesive loci' mentioned is capable of representing these basic quantities for the electron and photon (for example) as functions of linear and planar area distribution of such cohesive force; and is further capable of explaining in those terms the essential physical basis of QED.
So, you see, the most fundamental and indeed the only real self-evident or axiomatic truth which can be conceived in the human mind is that of the inviolate universal unity of existence; from which it follows that it is comprised of a singular substance, motivated by a singular cause, process and will (or 'metaphysical will' as Schopenhauer puts it); and indeed that it is the singular 'cohesive force' operating exclusively and distributed throughout it which is its most fundamental conceivable property. 'Energy' is one function of its 3-D distribution.
That of course, along with the rest of the above, is only my opinion; of which, if you are at all interested, you may find more elaborate expressions if you look.