In the simplest sense of it, the Free Energy is the heat of the system minus the compulsory heat loss due to entropy. So, in short, it is the amount of "energy" left over in the system, after we consider losses due to entropy. So basically, some amount of heat is wasted, and the remaining amount is useful. And, this remaining amount is the Gibbs Free Energy.
$G=H-TS$, here $H$ is the amount of energy which is contained in the system, and $TS$ is the amount that will inevitably be wasted. ThatsThat's how it makes sense to me anyway.