From a mathematical point of view it is understood as a consequence of Noether's theorem, which states every continuous symmetry of a physical theory has an associated conserved quantity; if the theory's symmetry is time invariance then the conserved quantity is called "energy".
It is understood as a consequence of Noether's theorem. This was from a mathematical point of view. Every continuous symmetry of a physical theory has an associated conserved quantity. This is what Noether's theorem states. The conserved quantity is called "energy". The theory's symmetry is time invariance then.