The reason a voltmeter can measure potential difference is the tiny amount of energy it requires to make the reading.
The voltmeter has a theoretically infinite or very large resistance, especially compared to that of any circuit it will be measuring.
This is because the person measuring the circuit voltage does not want to effect his readings by adding another impedance (resistance) into the circuit. Due to this restriction, the voltmeter coil must be very sensitive to voltage changes so that its sample of the voltage is insignificant to the circuit operation.
This is accomplished by using a very fine wire coil on a pin type axis like a compass. The coil in this case is housed inside a magnet in an assembly called a galvanometer. It is actually reading the voltage drop across the huge resistor in the meter which draws only a minute amount of current.
Most meters have steps of resistor values for reading different levels of voltage. Digital meters work the same way using electronic detection circuits rather than coils.
In this way, the voltmeter can read the circuit voltage without affecting it.