Those are in-ear monitors.They are usually custom made speakers that are worn by musicians and performers for theater, concerts and other various professions.
With an in-ear monitor, its just like an earphone you use with your I-pod, but the musician is receiving sound from the stage, the band, stage cues or whatever the musician wants.
On stage, it is very difficult to hear what is coming out of the main speakers that are projecting sound to the audience. This is because the mucisians are typically behind them, as well, the stage volume is usually very loud.
Singers and performers and even stage crew need to be able to hear specific feeds of sound in in order to sing, play or move appropriately on the stage.
Stage speakers or more commonly known 'floor wedges' have a tendency to make a screeching sound.This is because the microphone and floor wedge have come too close in proximity with each other. The sound from the floor wedge is amplified repeatedly through the microphone and has what is know as an infinite loop or feedback. When in-ear monitors are used properly, feedback usually does not happen.
In-ear monitors are used with a belt pack which is usually wireless. This prevents people from tripping over cords, and the ultimate in mobility when a performer wishes to move around or even body surf.