The outputs of a sound board are typically line level signals which can not directly drive speakers. Thus, a power amplifier must be used between the outputs of a mixer and the speakers. Power amplifiers come in a variety of sizes, each with different capabilities and features.
Power amplifiers are functionally simple units.
Most have a power switch and volume controls as well. The outputs of a sound board are typically connected to the inputs on the amplifier, and speakers are connected to the speaker outputs. The job of the amplifier is to take the small line-level signal and boost it to the levels required to drive speakers. One characteristic of better amplifiers is that they more faithfully reproduce the small signal at the speaker outputs. Inexpensive amplifiers tend to color the sound by inaccurately reproducing the line-level signal at the speaker outputs.