The Easter Egg has many meanings

The white color, represents the white marble tomb, where Jesus Christ's body was laid after He was taken down from the Cross. Also the egg is a symbol of life. From the tomb life came out, the Risen Lord.

DYING THE EGGS RED.
THE GREETING " CHRIST IS RISEN-TRULLY IS RISEN".

The orthodox faithful dyes the eggs red because the Roman soldiers put on Jesus Christ a red cloak, as King of the Jews, while they were mocking and torturing Him.

There is also a recorded historical event and a miracle that happened 2 years after the resurrection of Christ, outside Jerusalem.

Mary Magdalene was carrying a basket full of white eggs. She heard the new governor after Pontius Pilate will be passing from there. On the middle of the road she put the basket full of the white eggs and stooped the Governor saying:



"Welcome to Jerusalem oh Respectful Governor! I wish you will be righteous to the citizens of Jerusalem and will not be unrighteous like your predecessor Pontious Pilate. He, in vain, crucified the Son of God, Jesus Christ. He was threatened and He put Him on the Cross and He resurrected on the third day"