dnd 5th – How is the power of a magic object measured according to the rules?

Premise

The DMG establishes a relationship with the power of a magic object, its rarity and its character level.

Scarcity provides an approximate measure of the power of an object compared to other magic items. Each rarity corresponds to the level of the character.

He immediately follows with an example

A character usually does not find a rare magic object, for example, before the 5th level.

Question

The rules seem to have some sort of definition of what power means. What is it?

Reasoning

A number of questions seem based on the estimation of the power of a magic object. For example: