An amplifier is an electrical device which takes a small signal input and generates a large signal output that is reasonably faithful to the input.
Typically, the input signal will be from a low voltage, high impedance source, and the amplifier output will be high voltage and low impedance (especially when being used in an audio processing setup). For example, the magnetic mechanism in a microphone, electric guitar or record player produces a very low electric current and would be inaudible as a sound signal. Instead the current must be fed through an amplifier before being passed to audio speakers. Amplifiers of this kind invariably involve potentiometers to adjust the volume (or 'gain') - the degree to which the signal, and hence the sound, is amplified.
Many specialized amplifiers are used for various tasks, for instance, taking the signal from the final compressor in the signal chain at a radio station control room and boosting it to be fed to the broadcasting antenna. Such amplifiers have output impedances that are carefully tuned to the antenna's characteristics to ensure maximum power transfer.
An amplifier circuit is used in microwave ovens to produce the high power electromagnetic waves that do the actual cooking.