I was about to elaborate upon Planet Minecraft's diamond (system), but okey.
I will, however, use some of the previous posters' comments as basis for my statements.
Lola said, "Diamonds are rewards for the hard work and effort..." Removing the further part, they are indeed rewards for hard work and effort. After all, they are one of the most difficult elements to find in Minecraft, aside from a few. They are basically at the same level of hard-work as Nether Fortresses or End Portals.
Diamonds are the ingredients needed to possess the strongest tools and armour in the game; tools and armor that can withstand well over 1000 hits without any unbreaking enchantments.
Diamonds' bright blue shine and distinct color set it apart from the other materials in the game. A diamond-fitted player stands out a lot greater than an iron one.
Diamonds are hard to find. With their presence only being in levels 5-12, most prominently in levels 8-12.
With all of that being said, emeralds are some of the most underrated gems in the game xD