Diamonds are vanilla items, dropped when Diamond Ore is mined. They can only be found at layer 1-16 in a map. They are considered extremely valuable as they have 1562 uses opposed to iron, which only has 251. Diamonds can also be obtained through Macerating Nether Diamond Ore. Doing this will give you 2 diamonds, as opposed to smelting it, which will only give one.
Or when you have RedPower2 installed