An operational amplifier, or op-amp, is an electrical circuit incorporating a transistor, used to increase the power of an electromagnetic input signal such as a radio frequency or a wired electrical waveform. This increase in power, specifically by increasing the voltage amplitude of the signal, is called "gain", and an op-amp placed into an electrical circuit for this purpose is called a "gain stage".
In professional audio and video, these op-amps are used in virtually all aspects of signal processing, and often occur several times within a single piece of equipment. However, as referred to by the end audio user, two primary pieces of equipment, or conceptual sub-pieces, are called "amplifiers"; the preamplifier and the power amplifier.
A preamplifier or pre-amp is primarily a "tone-shaping" tool. A raw input signal, such as from a microphone or instrument, is input into the preamplifier, which first boosts the signal to a strength that the rest of the processing circuit can easily work with. The signal then normally passes through an "equalizer", which adjusts the relative strength of various individual frequencies of the signal, usually configurable by the operator. This equalizer can be as simple as a treble and bass knob, or as complex as a multi-band graphic or parametric equalizer. Finally, a second gain stage boosts the signal to the desired output strength. This signal strength is usually still relatively low (fractions of a volt).
The power amplifier is designed to take the "line-level" low-voltage signal and transform it into a "speaker-level" high-voltage signal, that then "drives" the cones in the speaker cabinets to produce the amplified sound in the venue. The basic idea is the same as a signal-level gain stage, but instead of a boost of a few tenths of a volt, the input signal is strengthened to many hundreds or thousands of volts.
Both of these types of amplifiers are basic necessities of any pro audio system. A mixing console or soundboard has several preamplifiers in its design, one for each input channel, that then feeds "buses", which can be independently controlled to produce the output signals. These mixer outputs are then fed to power amplifiers that feed various sets of speakers in the main system, or to radio transmitters that convert the electrical signal into radio waves that can be picked up by receivers.
Instrument amplifiers typically used on stage often have both a preamplifier and power amplifier in the same piece of equipment; this is normally called an "amp head" and is paired with one or more speaker cabinets to produce the instrument's "stage sound". When an amp head is placed in the same cabinet enclosure as one or more speakers, the setup is called a "combo amp".