The amplifer is an essential if often overlooked link in the recording chain. 
Although rarely fiddled with - if not operating correctly  you may not hear your work accurately reproduced.
The function of the amplifier, as its name implies, is to amplify the signal passed to it by the mixer. 
It is usually a two channel or stereo device providing separate adjustments for the level of each channel.  These are usually set to achieve a balance of level between the two monitor speakers when a signal of equal level is sent to both channels. 
See Also:
cables & connectors