What is the function of a variable resister in an electrical circuit?

A variable resistor usually has three terminals, one of which is connected to the 'wiper' by which means its resistance is measured.

By using all three terminals, we can control the potential difference in a circuit. When used in this way, we call the variable resistor a 'potentiometer'.

By using two of the three terminals, one of which must be connected to the variable wiper, we can control the current passing through circuit. When used in this way, we call the variable resistor a 'rheostat'.