Definition
Energy is never created or destroyed. It only changes form and moves around. When you add heat to something, that heat either builds up inside it or gets used to do work on the outside. Add the stored share and the used share together, and you always get exactly what you put in.
Your allowance ledger always balances
Say you get $50 in allowance this month. You spend $30 at the stationery store, and $20 is left in your wallet. Add what you spent to what's left, and you get the amount you started with.
That's because money doesn't appear or vanish on its own. It just moves from one place to another, and the total stays the same. So when a ledger doesn't balance, we go hunting for the item we missed.
Energy works just like this allowance ledger. Put a pot on the stove, and the heat going in either builds up in the water or goes into pushing the lid up. Some of it also escapes into the air around the pot as heat. Energy that comes in either builds up or goes out as work or heat, and it never disappears.
That's why physicists pick the thing they're studying and treat it like a single wallet. They write three lines side by side: the heat that came into the wallet, the work that went out of it, and the share left inside. Once you fill in all three, the ledger always balances.
Why no machine can work without fuel
Picture a wallet that never receives any allowance and only ever pays out. It might last a few days, but sooner or later it runs dry. A wallet that only sends money out and never takes any in can't exist.
A machine that supposedly keeps working forever without any fuel is called a perpetual motion machine. It's the same story as that wallet that only spends. It has to get usable energy from somewhere before it can turn a wheel and do work.
Take apart the gadgets that claim to be perpetual motion machines, and you'll usually find a hidden deposit. It might be a spring wound up earlier, a temperature difference between inside and outside, or a battery tucked out of sight. Once you balance the ledger all the way through, the empty line gets filled in.
So whenever a new perpetual motion invention shows up, people look for the deposit line first. If there's truly no place for energy to come in, the machine can't keep doing work on the outside. Any device that keeps working has a deposit line hidden somewhere.
A little more precisely
To be a bit more precise, a balanced ledger doesn't mean scattered money is easy to collect again. If you tossed your allowance out a dollar at a time all over town, the total would be the same, but getting it back would be extremely hard.
Energy is the same. When a car drives, the energy stored in the fuel spreads out into the wheels, the air, and friction heat on the road. The total hasn't changed, but it has turned into a form that is hard to gather up and use again.
That's why this law alone can't tell you which direction a change will go. If there are two ways for the ledger to balance, a different rule tells you which one actually happens.
There's one more footnote. When atomic nuclei split or fuse, mass has to be written down as a form of energy too. Once you add that share to the ledger, the rule still works perfectly.
Common misconceptions
Energy gets used up, so we have to save it.
Energy doesn't disappear. It only changes form. What we're really trying to save isn't the total amount, but energy that's gathered in a form that's good for doing work.
As technology improves, we'll eventually be able to build a machine that works without fuel.
We can cut down on the share that leaks away. But a machine that keeps putting out work without any energy coming in can never be built, because its ledger wouldn't balance.
Where you meet it
When you rub your palms together quickly, they get warm. The energy you used to move your arms didn't vanish. Friction turned it into heat.
An electric rice cooker turns electricity into heat to cook the rice. That heat then moves into the rice and the kitchen air and spreads out.
In one sentence
Because energy is never created or destroyed and only changes form, a machine that keeps doing work on the outside without taking in any energy can't be built.