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Mainly for two reasons:
1) They work great as a means of transaction (currency) because they are rare and their total amounts are limited. This means that their value is stable and inflation is impossible.
2) Contrary to paper money and electronic money, things like gold or diamonds also have a use value besides having an exchange value. In other words: you can't just use them to pay your lunch, you can also actually use them. Especially gold is extremely versatile. You can make a nice wedding ring out of gold but you can also use gold in many different scientific and technological contexts. For example the hard drive of your computer contains small amounts of gold. Every smartphone that comes from a big brand (apple, samsung etc.) contains so-called rare earth elements (which are usually extracted by appalling slave labor in the third world). Paper money on the other hand is in itself completely useless. You can't use a 10 dollar bill for anything... except maybe for lighting your cigarette if you're very rich. It's just a strip of paper.