Rarities have a serious role in items and trading in general. One may find rare items or common items, and rarities are used to describe whether or not the item is rare or common.
Common items are fairly simple. They can be found in ordinary chests and in shops for a small amount of Lamina or Aurem. They encompass the majority of the game's items.
Uncommon items are near-impossible to not come across by Level 60. They're as easy to obtain in chests as Common items, and can be bought in some shops like Cumulus Island.
Rare items are harder to find. They're generally items dropped from lower level bosses or clothing based on recurring NPCs (i.e. Nicholas' Top Hat).
Exotic items are very rare. They're mostly shipwreck items like Holden's Hat, but can also be re-colored and re-textured versions of previous items, like the Emerald Captain's Cloak.
Legendary items are incredibly rare, and the conditions for obtaining them are intense, like completing certain quests, to having paid to play the game, to fishing, to killing a boss a ridiculous amount of times, to solving an ancient, 1000-year-old riddle and going to the bottom of the sea in order to get it while having literally every other player in the server after you.
Holiday items. 'Nuff said.