The message written on Thorin's map was in moon runes (aka moon letters). Some moon runes could be read beneath the light of any moon, but some (such as the script on Thorin's map) could only be read by the light of a specific moon. The particular moon they needed (a crescent moon on a midsummer's eve) did not make an appearance until the Dwarves were in Rivendell, which is why they did not see the message until Elrond was examining the map. Moon runes were written in a special substance called Ithildin, which was made from the metal Mithril, which is why they were only able to be read by the light of the moon.
Another reason Elrond could read the map when the others could not is that he knew ancient Dwarvish (Elrond was very old and wise, and he knew many languages and things), but the other characters were unfamiliar with the language.