what does the use of symbolism contribute to the story
The use of symbolism in "Young Goodman Brown" is significant enough to allow readers to interpret the story allegorically. Thus, the characters, the setting, and many objects have figurative meanings in addition to their literal ones, and this creates a new level of meaning to the story as a whole. It is no longer just about one man who loses his wife, Faith, but, rather, it is about the danger to any Christian who takes God's grace for granted.
In the sense that this story can be read allegorically, the use of symbolism contributes quite a bit. An allegory is a text that has at least two layers of meaning: one is the literal plot, taken at face value, and the other is a figurative layer, a meaning that the text acquires as a result of the one-to-one symbolism of characters, objects, and places in the story. An allegory is often a literal representation of something that we ordinarily think of as intangible. Goodman Brown, for instance, is a literal character, might we might interpret him symbolically as a kind of "everyman" Christian: his common last name as well as the typical-for-the-1600s appellation of "Goodman" (which was like "Mister") seem appropriate. As a Christian, he thinks of himself as a good man, but we are, evidently, meant to interrogate this assumption. His abandonment of his wife, Faith, at home hints at her symbolism: she can be interpreted as a representative of his Christian faith, which he first neglects and later intends to exploit after this "one night" of sin, and he eventually loses her altogether in the end (never able to enjoy the peace she once brought him). Her pink ribbons can be read as symbolic of the innocence and purity associated with Faith/faith initially, and they are lost when Brown goes into the woods (when he has lost his faith). The forest, the snake staff carried by the devil, and so on, can all be interpreted as symbols in this way, adding a whole other layer of meaning to Hawthorne's story: when a Christian intentionally abandons his or her faith, even for a short while, he or she may lose the gift of God's grace forever.