The white stone is an ancient ritual. Back in the time when Jesus was teaching and someone served time in prison or in bondage of any kind, they were given a white stone when they were released. Each of us comes from bondage today, and we are being given a white stone to signify our freedom.
This ceremony comes from Revelations 2:17. In Revelations, John talks about the people being given a new name. ‘Let anyone who has an ear listen, to what the Spirit is saying to the churches.’ (The churches were those people whose thoughts were turned towards God.) ‘To everyone who conquers I will give some of the hidden manna. To all who see beyond the appearances, I will give all that is needed to live.’