Because this place in Germany has literally millions of diamonds (3 floors worth +) and they keep them so they maintain a rare status and so people will continue to pay so much to obtain them. They are actually not rare nor hard to come by. Just greedy business people taking advantage of us plebeians. Other than that, they are the hardest solid known to man and are very shiny and beautiful.
Some for the beauty of them, though you can get beautiful crystals for less. Others at least partially consider them an investment, knowing that other people will buy them in return in the future, and hopefully for more.
Diamonds are precious stones that form from coal after millions of years of heat and pressure. Due to the long length of time to create them and the supposedly small amount there is on the Earth, it has become very valuable and people tend to want valuable, attractive items.