Do we have a better understanding of what energy is since Feynman's time? When lecturing about conservation of energy in the 1960s, Richard Feynman remarked:

It is important to realize that in physics today, we have no knowledge of what energy is. We do not have a picture that energy comes in little blobs of a definite amount. It is not that way. However, there are formulas for calculating some numerical quantity, and when we add it all together it gives “28” —always the same number. It is an abstract thing in that it does not tell us the mechanism or the reasons for the various formulas. [1]

50 some years later, have we made any progress in terms of understanding the fundamental nature of what energy is?
 A: I can misquote:
"It is important to realize that in physics today, we have no knowledge of what space is."
What we know at present is that energy is part of a coordinate system defining a Lorenz four vector, the same way that space and time define another four vector.
We have a system of differential equations and the necessary mathematical tools to be able to model observations and data consistently and predict measurements for new setups successfully.
When one has an axiomatic mathematical theory, one accepts the axioms . Questioning them makes no sense, since they are necessary for that particular mathematical theory.
Lorenz invariance and coordinate systems, together with the postulates of quantum mechanics are necessary extra  axioms introduced into physics theories for mathematically modeling   data, the models also predictive of new experimental measurements. That is where our knowledge is at present.
Energy is defined as one of the coordinates of the energy-momentum vector. If this is progress from 60 years ago, I cannot tell. I can tell that further meditations belong to philosophy and metaphysics.
A: I suspect he was saying that we are in the same predicament 19th century physicists were in about understanding temperature. During the 19th century, the laws of thermodynamics, which included temperature, were defined and validated even though there was no understanding as to the source of temperature. At that time, no reliable scientist believed in the existence of atoms. It was only after the beginning of the 20th century that Einstein, Bohr and other physicists proved the existence of atoms and molecules and showed that temperature is the result of their random motions. We currently have no similar understanding as to the source of energy
A: I think Feynman's point was that there is no fundamental blob of energy (or a physical constant) which all other blobs can be explained as a multiple of.  Perhaps he had in his head the successful example of angular momentum where every blob of angular momentum in the universe is understood as a multiple of the fundamental constant $\hbar$ via the math of the rotation group.
In the years since Feynman's passing (Feb, 1988), we still have 3 generations of quarks and leptons, but neutrinos are no longer massless and the Higgs has been discovered, so the zoo of seemingly fundamental blobs of energy has changed/expanded...but there is still no theory successfully relating all the blobs to a fundamental constant of energy.  Feynman knew about the one energy constant, the Planck mass, that can be constructed from our fundamental constants ($m_{Planck}=\sqrt{\frac{\hbar c}{G}}=10^{19}\quad GeV$) but like everyone else could not calculate (~1 GeV) elementary particle masses from it. Perhaps the measurement of a non-zero Cosmological constant (which might actually be constant in space and time?) qualifies as a bit of progress since we now have a second energy constant ($\hbar c \sqrt{\Lambda}=10^{-42}\quad GeV$) to try to explain particle masses.
A: Energy is electrostatic motive force carried by moving matter and vibrating electrons/atoms.
Energy must coexisting with matter. Therefore there is no light wave, no photon particle traveling in space at light speed.
All theories based on light speed in space is C are mistaken. 
