The nylon earloop is used to create ear rigs for wireless microphones on actors. Designers will typically attach the microphone to the loop using hellermann sleeves and a hellermann tool (available here).
By mounting the microphone this way you get a consistent element placement on the actors face from performance to performance.
Some designers use a piece of elastic tied around the round loop to the bottom for a more secure fit, and some clip off the round section for a more invisible look. Up to you. These are resuable from show to show.