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:

"Christ is Risen-Truely He 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.

References by Archdiocese of America, Monachos and the V. Rev. Archimandrite Alexander Kile.