Where the liquid-pressure equation comes from

Take an imaginary upright column inside a stationary liquid. Its cross-sectional area is $A$ and its vertical height is $\Delta h$. Here $m$ means the column's mass and $g$ is the acceleration of free fall.

The liquid's pressure is greater at the bottom than at the top. The difference between those pressures supports the column's weight.

$p_{\text{top}}$ and $p_{\text{bottom}}$ are the pressures at the column's top and bottom. At rest, upward force balances downward forces:

$p_{\text{bottom}}A - p_{\text{top}}A = mg$

Divide by the same cross-sectional area $A$. The left side becomes the pressure difference $\Delta p=p_{\text{bottom}}-p_{\text{top}}$:

$\Delta p = \dfrac{mg}{A}$