This term has several meanings as applied to audio and video technology.
In a recording environment, monitors are the loudspeakers used to play back the live signals and recorded tracks of a project. Monitor also refers to a special mix (monitor mix) that is provided to the talent, usually through headphones, to give them a reference to the music they are performing. This is sometimes called a cue mix.
In sound reinforcement, monitors refer to the system of loudspeakers and/or in-ear systems that transmit an often-custom mix of the audio program back to the performers.