Kinyan L'Shabbos (published weekly by Hamodia) - July 18, 2012, page 11 has a fascinating article by Rabbi Avraham Y. Heschel regarding an ancient custom of displaying ostrich eggs in a Beis Knesses. Seemingly an ostrich, unlike other birds, does not sit on its eggs but keeps them warm simply by gazing at them from a distance. It mentions it in the name of HaRav Yaakov Emden Zatzal and explains that the reason is that they are meant to remind the Mispallelim of the awesome power of looking at something, and to inspire them to concentrate on Davening and not look in other directions.
It also mentions three reasons from the Sefer Midrash Talpios by Harav Eliyahu Hakohen, author of the Shevet Musar.
It is to remind us that in order for our Tefillos to be accepted, Kavanah is key. Therefore the eggs are present to remind the Mispallelim to ensure that nothing may interrupt our prayer and thus stand between us and Hakadosh Baruch Hu, Whom we are addressing personally.
The eggs symbolize the fact that the Eye of Hashem (so to speak) is at all times focused on Klal Yisrael. Nothing can possibly get in the way of this Hashgacha Pratis. Like the eggs that hatch only through the continuous surveillance of the mother ostrich. whose gaze must be continuous without distraction or interruption, or else the chicks will not survive. so we owe our survival solely to the constant Hashgacha of Hashem.
A Beis HaKnesses is a Mikdash Me'at, and placing the ostrich eggs there serve as a reminder of the fact that the Torah tells us (Devarim 11:12) that the "Eye of Hashem" is always watching Eretz Yisrael, and this in turn inspires us to Daven for the Geula and the rebuilding of the Beis Hamikdash.
This article from Bar Ilan University has more information regarding this Minhag.
Has anyone ever seen ostrich eggs in their Shul? If not why was this Minhag discontinued?