Diamond is a type of gemstone mined by the people of District 1. Because of this, District 1 is one of the wealthiest districts in Panem and is adored by the Capitol. According to Katniss, there is a machine in District 1 that can turn graphite into diamonds.
They were used to decorate the settings at Katniss' photo shoot modeling wedding dresses in Catching Fire. They were also used on tribute's chariots during the opening ceremonies. The dark blue dress Katniss wore to her tour in District 2 was studded with diamonds, and was jealously described by Johanna Mason in Catching Fire.
In the Capitol, diamonds are expensive, but popular. In the districts, except District 1, citizens wouldn't dream of having diamonds, because of their ridiculously expensive prices.
In The Hunger Games, Effie Trinket, the District 12 escort, mistakenly says that putting pressure on coal turns it into pearls, not diamonds. In Catching Fire, Peeta quotes her after he finds a pearl while diving for oysters.