How do louder sounds have more energy?

The way a hard bang on the table is louder than a soft one is a matter of AMPLITUDE.

In a simple description: the louder bang needs a higher arm movement (maybe a more angry face) than the softer one.

Sounds can be mapped as WAVES (they are a special type of wave but we won't go into that here) if you look at a typical wave, the loud sound will have more AMPLITUDE which means that the peaks and troughs will be further away from each other - and the soft sound will be close to a straight line.