"a saying or doing again, or over and over again; repeated utterance or occurrence," late 15c., from Latin iterationem (nominative iteratio) "a repetition," noun of action from past-participle stem of iterare "do again, repeat," from iterum "again," from PIE *i-tero-, from pronominal root *i- (see yon).
i.e. means that is to say, & introduces another way (more comprehensible to the hearer, driving home the speaker's point better, or otherwise preferable) of putting what has been already said; it does not introduce an example, & when substituted for e.g. in that function ... is a blunder. [Fowler]