do the symbols in the scarlet letter foreshadow the events? how do they help the characters understand their lives and how do they help the reader understand hawthorne's book?

This is a loaded question so I'll deal with one symbol, the most obvious one.

The scarlet letter is meant to be a symbol of shame, but instead it becomes a powerful symbol of identity to Hester. The letter’s meaning shifts as time passes. Originally intended to mark Hester as an adulterer, the “A” eventually comes to stand for “Able.” Finally, it becomes indeterminate: the Native Americans who come to watch the Election Day pageant think it marks her as a person of importance and status. Like Pearl, the letter functions as a physical reminder of Hester’s affair with Dimmesdale. But, compared with a human child, the letter seems insignificant, and thus helps to point out the ultimate meaninglessness of the community’s system of judgment and punishment. The child has been sent from God, or at least from nature, but the letter is merely a human contrivance. Additionally, the instability of the letter’s apparent meaning calls into question society’s ability to use symbols for ideological reinforcement. More often than not, a symbol becomes a focal point for critical analysis and debate.

AS far as foreshadowing events, the letter serves many purposes in terms of character exploration. Hester's long journey to redemption as well as Dimmesdale's long journey to man-up and confess his part are wrapped up in the symbol of the letter.