Short draft of a possible revised description:
Arc Words are a thematic phrase or set of words encountered several times during a story or an arc of a longer story, but outside the arc they are not encountered at all or only sparingly. The words serve to bring a sort of unity to the arc, and are usually encountered independently of any specific character or situation. However, they must carry some sort of dramatic or storytelling purpose.
Arc words can serve several different purposes in a story. They can help to reinforce a theme, or be used for humorous or stylistic effect. In some cases they can be nonsense [note: unsure about this sentence]. In the case where the meaning of of the words pose a mystery but are explained late in the arc, it's a case of Enigmatic Arc Words
Compare Catch Phrase
(a phrase frequently used by a character or a group), Sharephrase
(similar to a catchphrase, but used by several characters), Ironic Echo
, and Meaningful Echo