What is a potential divider and what does it do?

The most common type is resistive division. Say we have a source of V volts and we wish to apply a portion of the V volts (aV where a is between 0 and 1) to a load of resistance R. We can place a resistor R2 in series with load R to drop off the unwanted part of the voltage V. The math is a = R / (R + R2). This only works if the resistors are constant. For a changing load other methods are necessary.

Say the load needs 5 volts and it draws 10 milliamperes at 5 volts, but the supply is 10 volts. The effective load resistance is 500 ohms. A 500 ohm resistor in series with the load would drop off the unwanted 5 volt excess.

Suppose the load changes by 10%, but we wish to hold load voltage to 5%. We can place a 500 ohm resistor in parallel with the load and use a 250 ohm resistor to drop the voltage to 5 volts. The voltage change is now only 5% for a 10% load change.