Both have to do with being able to hear what you're doing.

The singer needs to hear the track in order to sing to it when recording. If you use anything other than headphones you'll pick that up in the vocal mic.

Musicians moved to in-ear monitors because hearing everything through stage monitors kind of sucks. The speed of sound is really slow so you're hearing things coming from all over the place not perfectly in sync. In-ear monitors fixes this, the whole band gets the perfect monitor mix wherever they are on stage.