Jesus says the disciples were betrayed by parents, brothers, relatives, friends, and some disciples were even put to death. This statement of His is that not a hair of their head will perish. The context of this statement speaks of some of the disciples dying, so this is not a promise that no physical harm will ever come. This could only refer to the resurrection.
The Greek word for "resurrection" means "a standing or rising up." The resurrection is a major theme of the New Testament teachings. Out of the 13 sermons in the book of Acts, 11 imply the resurrection.
The hope of the believer is the resurrection. The natural, earthly, corrupt, weak, mortal, body is said to be raised, changed and fashioned into a spiritual, heavenly, incorrupt, glorious, powerful, and immortal body. This is the completeness that has been purchased for all of us in Christ Jesus.
The Lord views everything in the light of eternity. Man tends to view things in the context of his brief life on earth.
From man's perspective, a person who dies for his faith in Jesus has lost a great deal. From Jesus' viewpoint, a martyr hasn't lost a thing. Even the very hairs on our head are numbered.
The patience that Jesus is speaking of is the calm assurance that God knows every hurt that we feel and He will abundantly compensate us in the resurrection. This knowledge helps us to control our emotions in the face of persecution instead of letting our emotions of fear dominate us.
