Dictionary definition
flagellation: beating with a whip or strap or rope as a form of punishment.
Self-punishment. It's an interesting concept. We do something wrong, and we beat ourselves up for it. Most people do this metaphorically, we replay the event over and over in our minds, tormenting ourselves. Other people, however, take self-punishment a bit more literally. They torture themselves physically, using their pain to repent their actions.
Interestingly, both Blake and White use the idea of self punishment in their work. The following lines are from the Visions of the Daughters of Albion:
"Oothoon weeps not: she cannot weep! her tears are locked up;
But she can howl incessant, writhing her soft snowy limbs
And calling Theotormon's Eagles to prey upon her flesh.
'I call with holy voice! kimgs of the sounding air,
Rend away this defiled bosom that I may reflect
The image of Theotormon on my pure transparent breast.'"
(Visions of the Daughters of Albion, plate 2, lines 11-16)
And from White's novel Riders in the Chariot:
"Most often [Himmelfarb] remembered those people he had failed: his wife Reha, the dreadful dyer, the Lady from Czernowitz, to name a few. Sometimes as he bored the hole, the drill grazed his flesh, and he accepted it."
(Riders, pg 266).
Both these characters, Oothoon and Himmelfarb seek to punish themselves physically. Oothoon desires stems from her torment at her love's anguish. Even though she was raped, she feels in part responsible for the behaviour of Theotormon. The lines "Rend away this defiled bosom that I may reflect / The image of Theotormon on my pure transparent breast.'" Show that Oothoon hopes that by physically punishing herself she is ridding herself of the rape. She believes that physical pain will redeem the tragedy.
In Himmelfarb's case, he seeks to harm himself as punishment for not doing more for the people he has cared about. He believes he has let down these people, and he feels that he deserves the pain that he is inflicting on himself.
People find absolution in different ways. Some people help others. Some people confess their sins. And then, other people use self-punishment.
Each to their own I guess....