Tungsten carbide is an alloy formed by combining tungsten with...wait for it...carbon. This gives the metal its renowned durability, while still being resilient enough to endure powerful impacts. In fact, it's one of the strongest materials out there, needing a diamond or other super-strong substances to cut it. Tungsten registers around a 9 on the Mohs scale, which is a measure of hardness; diamonds are a 10. This makes tungsten jewelry nearly impervious to scratching, meaning you won't have to remove a ring to do any kind of work that might damage other pieces of jewelry.
Because many people use "tungsten" as a shorthand, the term is often confused with tungsten carbide, but there isn't really any jewelry made of pure tungsten. Tungsten by itself is too brittle, requiring the carbon to make it strong enough to last. The jewelry marketed under either of these titles is very likely the same sort of material, either of which will include the carbon content to increase durability.
Because of the durability, tungsten is now used for a variety of jewelry, with laser engraving able to produce beautiful designs, such as the Masonic square and compass cut into the rings displayed below. The high scratch resistance of the metal ensures that the symbol will endure, remaining legible for...a long, long time.