As the name suggest they just source the sound from mixer and amplify it and then deliver this power to speakers which eventually drives them. The amplifier  output is measured in watts and they have an impedence range (measured in ohms) that they operate within. Usually each amplifier has two channels, right and left. Some manufacturers label them as A and B or one and two. Mismatching the amplifier with speakers can destroy the speakers (and also the amplifier). The most important thing to remember when choosing the amplifier is that its output matches that of speakers that you are planning to install. Speaker protection circuitry, EQ etc are added benefits. If you ever have to cheat on equipment because of cost considerations this is the place to do so. It is very difficult to  tell the sonic difference between two decent amps. The famous saying goes ... when recording concentrate on microphone, when installing a PA system concentrate on speakers. 

How do you match an amplifier to a speaker ... ? Let us take an example to understand the concept. Speakers usually have two ratings - RMS power and peak power, both measured in watts. An Electro Voice EVID 6.2 speaker has an RMS wattage of 300 watts and a peak of 600 watts. RMS stands for Root Mean Square. In layman terms RMS means continuous power or average power or normal power or effective power or 70% of peak power or whatever you may want to call it etc. Peak power is that wattage beyond which you will destroy the speaker. This is the maximum power input the speaker can handle that is being sent out by the amplifier. The idea is to get an amplifier which provides power / wattage more than RMS and less than peak power. The closer it is to the peak the better it is.


 Just like speakers, amplifiers also have ratings but instead of RMS they have impedence (measured in ohms) that determine the output. For example an amplifier will spit out 375 watts at 8 ohms and 500 watts at 4 ohms per channel. So if you connect one 8 ohm speaker to one channel it will get 375 watts of clean power. But if you connect two 8 ohms speakers in parallel to one channel then the amplifier will spit out 500 watts to both the speakers. This is because when you connect the speakers in parallel the aggregate impedence drops down from 8 ohms to 4 ohms making the amplifier work little harder. The lesser the resistance the more power will flow.

In theory you can connect as many speakers as you want by connecting them in the right combination of parallel and series connection to get within the impedence range of the amplifier. Since out speaker has RMS of 375 watts and a peak power rating of 600 watts we are safe connecting one speakers or two speakers in parallel. We cannot connect two speakers in series here as the aggregate impedence will be 16 ohms and it is out of range of the amplifier. The output power / wattage of the amplifier falls between the RMS and peak power that our speakers can handle. In theory you cannot drive the amplifier lower than 4 ohms otherwise they will overheat and eventually burn out. In practice we all do especially when there is no music involved. Please check the manufacturers documentation on the amplifier impedence range.

In case of a commercial (70 volt / 100 volt) amplifier the rules are different. All speakers are connected in parallel and the aggregate wattage of speakers is added up and the amplifier has to provide equal or more than this aggregate wattage. The rule of impedence matching does not apply to a 70 volt / 100 volt system. Please refer to how a 70 volt / 100 volt system works section for more details. 

There are other things like slew rate, damping factor etc. You need not worry about them as we are only talking about speech / tilawat which is the least possible load on any amplifier and speakers. Do not break you back by buying (and lifting) those heavy old amplifiers that weigh like 30 pounds. Buy the new ones which are about 10 pounds and typically referred as "D Class" amplifiers.

Some good amplifier brands include Lab Gruppen, Crown, Ashly, Yamaha, QSC, Electro-Voice etc. Any other decent brand will be fine too. Just make sure you have the right output wattage to match to your speakers.