It's an Ebonite handle.
Ebonites are hard rubber products obtained by the prolonged vulcanization of rubber with large proportions of sulfur.
The important properties of ebonite are:
1. Toughness combined with hardness
2. Solvent and chemical resistance
3. Ease of machining
4. Glossy look
It looks and feels like a hard plastic. It is called hard rubber because it is a modified version of soft rubber but not having the nature of soft rubber.
Ebonite was the material of choice before the dawn of plastics. It was and still is used for fountain pen barrels and ink feeds, pipe stems, shaving brush handles, the mouthpieces of brass instruments, and many other applications. I have seen an Espresso tamper made of Ebonite.
It is resistant to most chemicals, especially soaps but tends to oxidize (dulling of the glossy surface and a whitish appearance). It is sensitive to UV radiation exposure and shouldn't be left in sunlight over extended periods of time.
Ebonite can be re-polished with pipe stem polish for Smoking pipes, since the higher priced stems are usually made of ebonite. I use Savinelli pipe stem polish to make the handle shine again whenever it is needed. It's a lovely material and perfect to use for a shaving brush handle.