The DMG states a relation to a magic item's power, it's rarity, and character level.
Rarity provides a rough measure of an item's power relative to other magic items. Each rarity corresponds to character level..
It follows up immediately with an example
A character doesn't typically find a rare magic item, for example, until around 5th level.
The rules seem to have some sort of definition of what power means. What is it?
A number of questions seem predicated on estimating the power of a magic item. E.g: