Need help explaining this circuit and how it is dimensioned and designed
The zenner limits the input voltage to the resistor ladder to 6.2V.  The resistor ladder divides the voltage up into discrete steps for comparison.

For each step sum the resistors above and below, then use the 6.2V as the input voltage (\$V_{IN}\$) to the standard voltage divider formula:
$$V_{OUT} = \frac{R_2}{R_1 + R_2}V_{IN}$$

\$R_1\$ is the sum of the resistors above the step point, and \$R_2\$ is the sum of the resistors below it.