A resistor in an electrical circuit causes an obstruction to current flow. As the name suggests the resistance of a variable resistor can be changed. This allows the current flow through a circuit to be controlled. It can be turned up and down.

The way this is done is fairly simple. A sliding contact on a long coil of wire or length of graphite changes the amount of material in the circuit. The longer the length in the circuit the higher the resistance and the smaller the current.

It might look like this:

and a commercial version like this:

In most cases the resistance material is shaped into a loop so that the whole thing is neater and smaller:

The standard circuit symbol is a box (like a fixed resistor) but with an arrow through it:

So using it simply to turn the brightness of a bulb up and down the circuit diagram would be: