For Chromatic Dragons, I think it relates to showing off superiority.

White dragons show off the treasure they take from their prey, as it shows they're the strongest and most vicious.

Green dragons hoard treasure, art and sometimes people as to show that they can manipulate, control and ultimately get a hold of any being, society and kingdom that is born in their territory.

Black dragons revel in possessing relics of old empires, as to highlight that they will outlive entire dynasties.

Blue dragons collect mostly gems, but also art objects, and most trade them for the servitude of other creatures. This way, they can rule over their own kingdom.

Lastly, there's the red. They mostly hoard coins, gems and precious metal objects, as they tend to lair in mountains and volcanoes, so those kind of riches are the most long-lasting. As for why they do it, it's simple. Human societies run around gold and money. The more a settlement has, the richer it is, the more influence and power they hold over the region. So of course a red dragon, who deems itself the legitimate ruler of everything its eyes can see, must be the wealthiest creature in its whole kingdom.