The Hylia Series is the collective title for the equipment in Breath of the Wild with a Traveler's, Soldier's, Knight's or Royal prefix.
As the World Level increases, items found in chests and held by enemies will be replaced with a higher grade item from the series - i.e., a chest which contains a Traveler's Sword when Link has just left the Great Plateau for the first time may contain a Royal Broadsword if opened instead after all four Divine Beasts have been freed, the Final Trial finished, all three Medal of Honors collected, all Test of Strength Shrines completed and many Lynels killed.
Items found lying around or purchased in shops never upgrade with world level. Note that, despite their resemblance to "Royal" weapons, the "Royal Guard's" weapons are not part of the Hylia Series.
List of items
These corroded weapons use the basic design of items from the Hylia Series. When fed to a Rock Octorok, they are spat out in the form of one of their Hylia Series counterparts in as-new condition. The level of item they become (e.g., Knight's) depends on the world level and RNG, not the design used for the rusty item.
These items share common prefixes with the Hylia Series, but are unique items which are not affected by the world level:
Traveler's Bridle (amiibo-exclusive)
Traveler's Saddle (amiibo-exclusive)