On stage, the monitors are usually wedge shaped speakers that point toward the performers. They are mixed to provide the sound that is not present on stage, usually vocals, keyboards, and other non amped instruments, although they often reinforce such instruments.
Larger concerts will have a monitor mixer and engineer that is off to the side of the stage with a special multiple bus console which is fed via a stage splitter. Smaller concerts use the auxiliary buses on the main console.
In studio, the monitors are both for performer and producer, the latter often using speakers called studio monitors and the former commonly using headphones. These allow both parties to hear the mix and, most importantly, allow the performer to hear themselves. The studio monitor speakers are used to mix down the performance, and to monitor the performer.
Common types are Stage Monitors, Studio Monitors, In-Ear Monitors, and Isolation Headphones.
"The monitors are feeding back!"