In distant regions likeliest to hold her
Our heroic speaker sets out to find this alluring Goddess which is hated by saints and sober men. He already knows that he has a long way to go and many obstacles to face to find her, but it is worth it because she is something they all want to know above everything else. She is an object of hatred and desire all at once.
Beyond the cavern of the seven sleepers
The speaker assumes that he might find the Goddess at the most dangerous places: at a volcano's head, among pack ice, or beyond the cavern of the seven sleepers. This allusion to the story of the seven sleepers is significant because it draws a connection to the different cultures where this story has a place in, concluding that this cruel, but magnificent goddess is an idea present among many cultures.
We forget cruelty and past betrayal,
Heedless of where the next bright bolt may fall.
These are the ending lines of the poem which mark the White Goddess, or Mother Earth, as a betraying and cruel feminine force. This figure still makes the brave men forget about this in her magnificent outwardly appearance and presence - foolishly, not thinking about the inevitable consequences.