It's a key item obtained by a Wi-Fi Event.
It allows you to catch the other Eon pokemon depending on your version.
Latios for Heartgold and Latias for SoulSilver.
If you take it to the Pewter Museum you will trigger a scene with Steven Stone where he explains to you that the Enigma Stone is actually the Soul Dew. After this Lati@s will battle you and will be in the same spot if you are not able to catch it on your first attempt.