A variable resistor is a component that has three connection points. The two outside connectors has a fixed resistance value and the connection point in the middle can be adjusted towards the one end of the resistor or towards the other end by turning the knob of the variable resistor. If the variable resistor is turned anti-clockwise till it stops the resistance between the bottom connection point and the middle connection point is 0 ohm. If it is turned in a clockwise direction the resistance increases until the wiper reaches the top end and then it will have the maximum resistance equal to the value of the variable resistor.
What is the difference between a potentiometer and a variable resistor? The answer is very little. A potentiometer is normally for low current applications and tends to be set at a value and then left alone like a trimmer. Potentiometers are of a lower quality because they only need to be set a couple of times with a screwdriver. Where as variable resistors are normally for higher current applications and are of a higher quality.
The most common use of this type of resistor is as a volume control in audio circuits but it can also be used as a potential divider or in any place where an adjustable resistor is required.