The first stage for input is the mixing board. These range from simple, with a few features, to massive surfaces covered with hundreds of knobs, faders and switches. The mixer amplifies the input signals and adds equalization to individual instruments and vocals. Outboard equipment like reverb and compressors connect through the mixer. Small mixers and turntables are essential for DJs.
The signal coming from the mixer is ideally the perfect blend of the performers, but it is at a quiet level, fine for headphones or sending to recording equipment. This signal boosts many times to fill a venue to a comfortable listening level. Power amps aren't glamorous. They do one thing: make it loud. Good amps will do so without coloring the signal from the mixer, and without distorting.
Mains speakers deliver the goods. In clubs, speakers may be simple, two-way cabinets (woofer and tweeter), perhaps with subwoofers for deep bass. Companies are marketing more speakers with their own integrated power amps, simplifying the set-up process. It's common at major concerts to have banks of speakers flown from rigging, or stacks of cabinets at each side. Crossovers divide signal for bass, midrange and treble banks for individual amplification.
Fold-back speakers and in-the-ear monitors allow the musicians to hear what they and their band-mates are playing. Monitor systems break off from the mixer and follow a similar path through amplifiers to speakers or ear buds. In the case of large concerts, a separate mixer might handle monitor system requirements, which may provide individual mixes to each musician.