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Latios and Latias are known as Eon Pokemon from their pokedex entries, I have for a long time wondered Eon that had to do with the due and after a bit of research I have concluded 'Eon' is most likely a mistranslation.
Firstly, as pokemon are games targeted mainly at children the japanese versions didn't use kanji in the text of the games so that children could read it easily until gen 5 added a option to have kanji in the text (however these categories from pokedex entries are still written in kana). However the lack of kanji causes ambiguity such as in this case.
Latios and Latias are described as むげん (mugen) pokemon. The most common word read this way is 無限 which meany infinity (thus Eon) but what does have infinity do to with Lati@s? I believe instead that the mugen here refers to 夢幻 which means dream, fantasy. Which fits the duo more than infinity.
In the Southern Island where you catch one of the due there is a message talking about dreams.
>All dreams are but another reality. Never forget...
The names of the bgm in ORAS used for soarign in the sky also refers to 夢幻. The one used during the day is called 天翔ける夢 (Soaring Dreams) and the one used during the night is called 天翔ける幻 (Soaring Illusions). As you can see the last kanji from each title form together 夢幻.
In general, I also think 夢幻 refers to their elusive nature as roaming pokemon.
