One of the Starting Gifts. Nothing more than a symbol of hope. This item appears to do nothing than create speculation and the chance that something may happen.
Dark Souls Game Director, Hidetaka Miyazaki has stated in an early interview that the player should select the Pendant or nothing as a starting gift (unable to verify source). This reinforces that idea that the Pendant does nothing (but hope).
In a later interview Hidetaka Miyazaki suggests that the Pendant may do something. A perfect return statement to keep the speculation alive. Below is part of that interview.
Question: In interviews leading up to Dark Souls’ release, you suggested that players should go with the pendant starting gift. There’s still a lot of confusion and mystery in the community surrounding what this item affects. Now that the game has been out for a while, care to give any further clues?
Hidetaka Miyazaki: Hm.... I am very happy to get this question because this is exactly what I expected. I am very sorry, I cannot tell you here how you use the item. I still want people to try investigating the meaning of the item. Please find it out on your own! [laughs]
Your first encounter with Rhea of Thorolund, the (possible) leader of the Way of the White Covenant, at Firelink Shrine.