Potentiometers are everywhere, but we seldom call them by that name. A potentiometer is essentially a volume control for just about anything. Often shortened to "pots" in some arenas, such as for musical instruments like electric guitars, potentiometers adjust an electrical signal up or down. Some potentiometers turn like a dial, while others slide up and down. They are sometimes called rheostats.
Potentiometers all have an adjustable spectrum. At one end of the spectrum the potentiometer is fully on; at the other end it is fully off or as low as it will go. The motion is sometimes linear, where the adjuster slides forward and back or up and down. Rotary dials are also very common, like a typical volume control. In addition, some potentiometers have a binary on-off switch. For example, many light-switch potentiometers click on or off if you push in on them. That gives the operator the choice of choosing off or anywhere on the spectrum of on.
Potentiometers are almost always electro-mechanical. They use a mechanical device to operate or adjust an electrical device. Other devices like a water faucet perform similar functions, but potentiometers generally refer to electrical controls, not hydraulic or other types of energy. The types of electrical and mechanical devices used varies widely.
While it can be accomplished in a number of ways, generally potentiometers increase and reduce electrical resistance. Resistance is the opposite of conductivity. It is the characteristic of not conducting electricity. Resistors are often used in electronics to meter current. You can think of a potentiometer as a variable resistor: It can be changed so that it is either more conductive or less conductive. In other words, it can be turned up or down.
The application of potentiometers is usually something more than just translating mechanical energy into different resistance characteristics. In other words, there's a point to it. For example, in a stereo the purpose is to turn the volume up. On an electric range, it is used to make the stovetop hotter. It can control servo motors that control any number of things. It is almost always a means of translating physical energy to adjust another kind of energy to serve a particular purpose.