in its simplest form, an amplifier (
http://en.wikipedia.org/wiki/Audio_amplifier and
http://en.wikipedia.org/wiki/Electronic_amplifier )is a device that takes a small signal, adds power to it, and outputs a larger signal that looks very similar(ideally it would be the same but this is not the case) to the small signal in amplitude.
different amps have different setups some use a two stage gain process
input -> voltage gain -> current gain -> output
by gain here we mean "adding"
Some use just a single stage that performs both functions.
Power is measured in watts, that is Voltage(in volts) x Current(in amps) = Watts
example: 12v x 500mA = 6 Watts
There are two measures of power/wattage in audio, Point to Point and Root Mean Square. The latter is a function of the former. Point to Point means the swing from the high point of the wave to the low point on the wave, RMS means (roughly) the average of the waveform. The latter is considered a more representative figure.
http://en.wikipedia.org/wiki/Root_mean_square
An opamp or operational amplifier (
http://en.wikipedia.org/wiki/Operational_amplifier ) is a logical block device used in one of the above devices. Specifically, in modern terms, it is an integrated circuit(
http://en.wikipedia.org/wiki/Integrated_circuit ) produced on a monolithic process on silicon.
This process allows great matching of values of components within the circuit, allows leaps in speed, due to shorter circuit traces, and optimisation of components. This allows large slew rates, better linearity and greater bandwidth than discrete components in high grade components.
The negative side of this is that due to mass production, it's usually a tradeoff due to a "one size fits all" mentality. This leads to slight differences in output sound/structure based on the scope of the intended use.
Another negative is it cannot handle as high voltages as discrete components due to heat disappation. As a function of this, many opamps have low current output current also, so they are most commonly used in the voltage gain stage of amplifiers, this suits the application as most of the time you don't need high voltage for audio applications, instead you need high current.
There are two main types of opamps, Bipolar junction input(
http://en.wikipedia.org/wiki/Bipolar_transistors ) and jfet input (
http://en.wikipedia.org/wiki/Field_effect_transistors http://en.wikipedia.org/wiki/JFET ) . The latter are easier to use due to their lower speed, and more stable/linear characteristics.
More information can be found in those links
