Diamonds being the hardest natural substance, can be used to carve, cut and polish anything, including another diamond. Their optical properties are also of value as high-quality, microscopic lenses that don't wear down.
Incidentally, they also look very pretty when cut and polished correctly, so people like jewellery and ornamentation made of them.
Diamonds have to be mined by humans
to cut other diamonds; to wear
Diamonds are the hardest material on earth, and 75% of diamonds mined are used in industry. Industrial diamonds are used for cutting tools.
Diamonds are a commodity at the gemstone level; and are used in tools at the industrial level (about 75%). Gemstone diamonds are expensive and are either given or purchased based on some emotional state of mind. (The same can be said about any other expensive commodity.) Industrial diamonds are used to fashion useful materials, structures and tools that benefit humans.
Dimonds are useful because its the hardest naturally occurring substace.
The humans who need water will buy water; humans who have access to water may choose to purchase diamonds.
Humans interested in power and money are responsible for conflict diamonds. Other names for these humans are war lords and terrorists.
Conflict diamonds are usually mined by humans digging in the soil.
We -- humans -- can manufacture diamonds. It takes enormous heat and pressure to produce man-made diamonds.
Diamonds are most 'useful' as industrial diamonds, attached to tools that require precision, tough cutting abilities and so forth.
Eighty percent of all diamonds mined are industrial diamonds, used in tools to increase sharpness, precision and useful life.
Humans mine for diamonds for the same reason that any human industry takes a natural resource from the earth: to make money.