Another way of looking at it, is that there is a conserved quantity, and we call it energy. A conserved quantity is a number you can calculate for a given system, "let it do stuff", and then calculate again the number and find out that it is the same.
It turns out that that conserved quantity is a sum of terms. And it happens to be so that "kinetic energy" is one of those terms. We can also chunk up "closed systems" in subsystems which interact with each other, and even then, we can assign terms of "energy" to the different subsystems. Some terms are "bookkeeping" terms, which add to one subsystem what they take away from others. Using this trick, you can then even say that the energy is conserved for the subsystems (but it is a trick: you used "bookkeeping").
So for the simplest of systems, the sum is just this single term. Energy = kinetic energy. As energy is conserved, this means that kinetic energy is constant.
For more complicated systems, say, a ball on earth, clearly, kinetic energy is NOT conserved. But "energy" is. We do that by introducing a "bookkeeping" trick, the "potential energy". It turns out that you can introduce a term in the energy sum of the ball, which takes into account the interaction between the Earth and the ball. The Earth itself has a similar term. The total energy of "earth + ball" is still not ok, you have to consider "earth + ball + gravity". And then the total energy is again conserved. But we don't want to work with "earth + ball + gravity". We only want to work with "ball". And there, the energy is "conserved" if we use "kinetic energy + potential energy(of gravity force)".
Now, as the ball falls through the air, we see that our sum is again "wrong". KE + PE is not conserved we find out. It turns out that that's because of the interaction with the air. There's friction. We can again get the balance right by adding yet another term: "heat".
And so on. Each time when we studied new systems, what we thought of being the "energy" seemed not to be conserved after all. But we could always manage by adding a new term that got the balance right. All these terms are "energies".
It looks like a stupid trick. Of course, if you add a cheat term each time your bookkeeping turns out wrong, you will get it right ! In a way, yes. But nevertheless, there are much less "cheat terms" than there are systems, so it is still a useful quantity. If we have a dozen or so "energy terms", that will be it, and we can describe gazillions of systems with it and it is "conserved".
But then there are more profound reasons to "know" that there is really a conserved quantity called energy, and that this is not some silly bookkeeping game. For one, energy is indeed related to the time translation symmetry of the laws of nature (that the laws are the same "today" than that they are "tomorrow").
edit: in fact, if you think about it (unless I'm making a silly mistake here), energy is the only strictly conserved continuous scalar quantity.
There are other conservation laws of course, but they are or approximative, or discrete, or not scalar (unless I'm overlooking something).
There's conservation of "mass". But it turns out that it is approximate, in relativity.
There's conservation of "atoms" in chemistry, but it turns out that nuclear reactions violate it.
There's conservation of baryon number. It seems to be exact for the moment, but it is a discrete number (an integer).
There's conservation of lepton number - again it is discrete.
There's conservation of angular and linear momentum: these are not scalar quantities but vectors/tensors.
There's conservation of charge (but that's again discrete, in 1/3 of electron units).
So energy is THE conserved continuous scalar quantity.
