When you're playing live you need to hear two things: 1. yourself, 2. the rest of the band. Traditionally this was handled with stage monitors, wedge shaped speakers on the stage...but this clutters up the stage impairing your mobility and its loud which will eventually damage your hearing...so more often now, musicians use IEMs connected to a wireless rig which gives them better mobility and protects their hearing. Often a band might want to play to a click track which works well with IEMs.

The monitor mix is pretty important, if it's not good you can have people playing too loudly/softly and singers singing out of tune. The mix also might not be what one would think of as good for listening to but it's good for monitoring.

Wearing IEMs does disconnect you a bit from your audience though. I've seen John Mayer playing wearing headphones only covering one of his ears.