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.