What is a potential divider?

A potential divider is essentially a series circuit. The characteristics of a series circuit is such that voltage from the source (a battery for example) gets split across the resistors according to the value of the resistances. 

An important consideration here is the value of the resistance. As a basic rule, the greater the resistance value, the greater is the voltage drop across that resistor. 

Mathematically, for a potential divider circuit with two resistances connected in series (say R1 and R2) to a voltage source (say VS), the voltage drop across R1 (VR1) can be found:

VR1 = (R1/(R1+R2))*VS

And likewise the voltage across R2, VR2 can be found:

VR2 = (R2/(R1+R2))*VS