Arthur Dimmesdale's back story is crucial to the theme. Since he is a respected minister with a secret sin, it highlights the hypocrisy in Puritan society. His internal struggle reflects how sin can corrode the soul even when it's hidden, which is a major theme in the book.
His back story shows the theme of hidden sin. His affair and the resulting guilt he hides contribute to the overall exploration of sin and its consequences in Puritan society.
Well, Arthur Dimmesdale's back story is deeply intertwined with the themes of 'The Scarlet Letter'. His story of the secret affair and the guilt that follows represents the idea that sin cannot be truly hidden. It will always have consequences, whether they are physical, mental or social. His position as a minister makes it even more poignant as it shows how even those who are supposed to be the most pious can fall prey to human weaknesses. His internal conflict also emphasizes the theme of individual conscience versus society's expectations. His inability to come clean about his sin for a long time shows how difficult it can be to go against the strict moral code of Puritan society, while his eventual confession at the end shows that the truth will always find a way to come out, no matter how long it takes.