Tungsten, derived from the Swedish words 'tung sten', meaning heavy stone; is a dense metal with an atomic number of 74. A very rare metal, its most important characteristics are its incredible density, hardness, and melting point. To make it clear: Tungsten has the highest melting point of any element, meaning that it requires the highest temperature to be melted. In addition, its 'tensile strength' is also number one among all elements known to man.
Tungsten is usually found in wolframite and scheelite, and raw tungsten by itself doesn't exist, so it has to be taken from within those rocks and minerals. The other name for tungsten is 'wolfram', from the 'wolframite' that it can be found in.
Tungsten as an element was not even hypothesized until 1781, when scientists discovered an acid called tungstic acid, which was produced using wolframite. Looking at the properties of this acid, scientists hyphothesized that it should be possible to produce a raw metal from this acid. Several years later, the first raw tungsten was successfully produced by reducing tungstic acid with charcoal, and so tungsten as an element was discovered.
Almost all uses of tungsten arise from its incredible hardness and resistance to scratching and melting. About half of all raw tungsten produced in the world (about 70,000 tons a year) is converted into Tungsten Carbide. Tungsten carbide is referred to as an alloy, but is technically a ceramic. It has even better properties than tungsten, with increased hardness, and is unbelievably hard.
Tungsten carbide's extreme hardness and abrasion resistance makes it very useful in the field of machining/cutting tools. In addition, because its melting point is so high, it can be exposed to a much greater degree of heat than other metals, which means that it's great for drills, because it allows faster spinning.
It's also used as a base for surgical instrument, even though they cost nearly 20x as much as other metals.
And also, of course, tungsten carbide is used to make extremely scratch resistant and durable jewelry. It can retain polish nearly indefinitely, and is estimated to be 12 times harder than 18 karat gold.
When in not carbide form, tungsten alloys are used in rocket nozzles, as elements of radiation shielding, and as a construction material in turbide blades. These are all due to its nature which allows very high amounts of precision to be applied onto it.
Both tungsten alloys and tungsten carbide are heavily used in armament manufacturing. It's extensively used as a 'kinetic energy penetrator', meaning it's used in things like armor piercing rounds and armor piercing cannon shells (like the SABOT shell), as well as missiles.