First, you have system with some joules, named $U$ by physicists. Some guy come near and say:

-- Whoa it is bad coz volume can change.

You say:

-- np, dude we add here $pV$. Our new energy is $H=U+pV$.

-- But hey, your temperature can change by external heat, you have to count that into also

-- np, we drop $TS$ from our energy, and rename it. $G=U+pV-TS$

Here you are.

People name it "available" energy, because if your system increase in size, it creates work. $V$ increase, so $U$ can decrease. But energy always have some limits to going down. When you drain everything you can, system goes into $G=0$.

You cannot drain all $U$ because you need eternal system with $T=0$.

First, you have system with some energy, named $U$ by physicists. You think you have all the information you need to characterize the system but then some guy comes near and says:

"Whoa, that's bad, the volume of your system can change."

You say:

"No problem, we just add here $pV$. Our new energy is $H=U+pV$."

"But hey," they say, "your temperature can change by external heat, you have to count that also."

"No problem, we subtract $TS$ from our energy, and rename it. $G=U+pV-TS$"

There you are.

People name it "available" energy, because if your system increases in size, it creates work: $V$ increases, so $U$ decreases. But energy is always bounded from below. When you drain everything you can, your system goes to $G=0$.

You cannot drain all $U$ because you would need an external system with $T=0$.

First, you have system with some joules, named $U$ by physicists. Some guy come near and say:

-- Whoa it is bad coz volume can change.

You say:

-- np, dude we add here $pV$. Our new energy is $H=U+pV$.

-- But hey, your temperature can change by external heat, you have to count that into also

-- np, we drop $TS$ from our energy, and rename it. $G=U+pV-TS$

Here you are.

First, you have system with some joules, named $U$ by physicists. Some guy come near and say:

-- Whoa it is bad coz volume can change.

You say:

-- np, dude we add here $pV$. Our new energy is $H=U+pV$.

-- But hey, your temperature can change by external heat, you have to count that into also

-- np, we drop $TS$ from our energy, and rename it. $G=U+pV-TS$

Here you are.

People name it "available" energy, because if your system increase in size, it creates work. $V$ increase, so $U$ can decrease. But energy always have some limits to going down. When you drain everything you can, system goes into $G=0$.

You cannot drain all $U$ because you need eternal system with $T=0$.