
Potential dividers are used for dividing up the voltage, so that a part or parts of a circuit only receive the voltage they require. Potential dividers consist of two or more components (usually resistors [resistors: components which resists or 'slows down' the current in a circuit by acting against the flow of electrons. Resistance is measured in ohms. ]) arranged in series [in series: connected to a circuit in such a way that the same current flows through each component in turn. Opposite of in parallel ] across a power supply.
The circuit diagrams below show three common types of potential divider: two fixed resistors [fixed resistors: type of resistor whose resistance remains constant. Opposite of a variable resistor ] in series, a fixed resistor and LDR [LDR: Light Dependent Resistor, or LDR, is a type of resistor which is affected by changes in light levels. A cadmium sulphide layer causes a decrease in resistance in the light and increase in the dark. ] in series, and a thermistor [thermistor: type of resistor that changes resistance with temperature - also called a Temperature-Dependent Resistor. Usually the resistance decreases with an increase in temperature (and vice versa) ] and variable resistor [variable resistor: type of resistor whose resistance can be varied to change the amount of current flowing through it. Opposite of a fixed resistor ] in series. (Note that the resistors are usually drawn vertically on a circuit diagram.)

a circuit diagram showing two fixed resistors arranged one above the other

circuit diagram shows an LDR and fixed resistor arranged one above the other

A circuit diagram, a Thermistor and variable resistor
Potential dividers are important in both transistor-switching circuits and op-amp comparator circuits [comparator circuits: circuit with a comparator - a component which compares two voltages or currents, amplifies the difference between them, and changes its output depending on the result of the comparison ]. The diagram shows a darkness sensor circuit with a transistor [transistor: components which do not conduct electricity unless they are turned on by a (different) electrical current. This means they can be used as switches, amplifiers and in other ways. ] used as a switch. When the LDR senses a drop in light, the LED is switched on.
When the LDR has light falling on it, its resistance is low - usually around 400 Ohms. When the LDR is covered up the resistance increases, (often to many kilo-Ohms). When the resistance of the LDR is small its share of the voltage supply is small too, so Vout from the voltage divider is small, and the transistor is switched off.
In the dark the large resistance of the LDR takes a large share of the voltage supply, so Vout is large and the transistor and LED both switch on.