The purpose of an amplifier is to receive the electrical signal from your source, in this case your turntable, and boosts that signal and forwards that signal on to your speakers which will use it to recreate the music.
Amplifiers have three basic connections: inputs from the source, an output to the speakers, and a source of power from the wall socket.
There are many types of amplifiers for different purposes. More channels are useful for surround sound, but music is mostly about just two channels. Good old stereo - you can't beat a great two channel system for music!
The more power the amplifier produces the better performance you will get from your speakers. Its a good rule of thumb to invest in an amp roughly around the same price as speakers, generally you'll find its a good match of amplifier power output to speaker ability.
Oh,and let’s dispel one popular myth right here and now. More speakers are damaged by trying to match them with an amp that has too little power, than an amp with "too much”. You can never have too much power!