It is my understanding that, according to this spiritaulity, when one sees the divine light, he is literally seeing God (in his energies but not his essence). Palamas argued in favor of the idea against Barlaam, because Palamas wanted to protect the truth that we really do participate in the divinity as we expereience theosis. One scriptural example that heyschasts argue is an example of Sts. Seeing the "Divine Light" is the transfiguration of Christ on Mt. Tabor. here the Apostles saw Christ in dazzling white light. Hesychasts believe that that light is the Energies of God and, thus, that the Apostles saw God.
While I certainly agree with the Essence/Energies distinction and the idea that we really do participate in the Divinity, I do not agree with Hesychast spirituality or the idea that one physically sees God because I am a Catholic. However, this is not the place to debate that matter so I will not do that here.