Loudspeakers are all around us. We are familiar with how easily they appear to fill up rooms of all sizes with all kinds of sounds.
A speaker by itself has only two terminals, usually labelled + and -, for electrical connections. The principle parts of a dynamic loudspeaker (as opposed to other types of speakers) are a coil of wire, a permanent magnet, and a moving paper cone. Mechanically, it functions as an electromagnetic motor. The parts are all passive and require a source of power if is to do anything useful.
A common dynamic microphone could be attached directly to the speaker's terminals. No matter how loud you sang into that mic, the speaker wouldn't move. You do create a small voltage when you sing into a microphone, but this small output has no ability to drive the speaker's electromagnet.
To give voice to a loudspeaker, a power amplifier must be used. As a generic thing, a power amplifier is usually thought of to be linear and, ideally, free of distortion. It usually has an input sensitivity measured in volts, and will be able to produce many volts of high power signal at its output.
A preamplifier is a generic term to amplifier circuits that come before the power amp. In preamp circuits, linear, distortion free performance is also good, but many kinds of desirable distortions and non-linear effects may be introduced on purpose.
The main advantage in performing signal processing in the preamp, instead of the power amp, is the savings in energy required.