This necklace is a relic from the long lost nation of Mu to which Matsuo Shin and Eiry traveled in Matsuo Shin and The Stones of Mu. Eiry found it there and unwittingly took it away with them in their hurried exit from the underground city.
Unlike the items which Matsuo found, it doesn't appear to have any unusual properties. After a few weeks wearing the necklace, however, Eiry began to notice a higher sense of intuition, and a feeling that the two were connected. Since no one has been able to determine anything about the necklace--it doesn't display or give off any properties--she resumed wearing it.
In actuality, like other artifacts from Mu, it has an amount of phsycic energy which raises the awareness of the wearer. However, there is so little of it that it is very hard to detect, and it is quite safe for regular wear. In fact, Eiry hardly ever seems to take it off.