Prophecies are similar to the quests that characters like Tarkleigh send you on, however they are less structured, less predictable, and can only be acquired from Navali in exchange for a silver coin. Prophecies can do a broad range of things. Some can guarantee that certain items will drop from specific monsters. Some add new monsters to areas, some drastically change the look of certain areas, and some grant avenues to new or upgraded unique items.
Sometimes you may get a prophecy that you don't want or need at that moment. Navali can seal such prophecies for some silver coins, turning it into an item that you can store in your stash or trade to another player.
While some prophecies can grant you access to powerful and valuable rewards, sometimes the prophecy IS the reward. Remember, you can end up fulfilling a prophecy without meaning to, so it's always worth considering spending some silver to save a nice crafting prophecy for an item that could greatly benefit from it.