The New-Hell Broom is a cleaning device used by Hell's cleaning department. The broom, however, looks more like a besom. This broom is most commonly seen being used by Elsie.
The broom can clean everything and anything so perfectly, it looks as if the surface being cleaned was just freshly made. The broom completely destroys any foreign contaminants and unwanted objects surrounding the surface.
The strength and power of broom's ability to annihilate foreign contaminants can also be controlled to destroy more resilient substances. A down-side to this, however, is that a careless cleaner (In this case, Elsie) can ignorantly set the power to maximum, providing enough force to destroy a small house.
Other than that, it appears to function as a normal Broom.
Sometimes in the manga and in the second opening in the anime, Elsie is shown to be sitting on the broom and seemingly being able to use it as a flying object. While in some European myths, brooms are often able to do that, it is currently still unknown if Elsie was really using her broom to fly or if she is using her flying abilities granted by the hagoromo.