Black Swan (Symbol)
The black swan that Hester is seen dragging through the snow is a symbol of death. Hester's own death is tied to the death of the black swan by a curse her mother placed on her. Thus, we can see the swan as a complex symbol of Hester herself, and of her own inevitable death by the end of the play.
Ghosts (Symbol)
Ghosts are a symbol of the past in the play. The ghost of Joseph Swane is a reminder of the crime that Hester committed, and comes to ask her more about the incident in Act 3. The ghost symbolizes the fact that Hester has some unfinished business in her past for which she needs to make amends.
Hester's Stubbornness (Motif)
While it is an element of the narrative, Hester's stubbornness and her refusal to leave the Bog of Cats, in spite of everyone's urging her to do so, becomes a kind of motif because of the repetitiveness of the play's structure. Time and again, characters do their best (or their worst) to convince Hester that she ought to leave, but she refuses, stubbornly laying claim to the territory in which she was raised.
The Bog of Cats (Symbol)
The Bog of Cats, the setting of the play, is itself a symbol for Hester's past and her origin. She feels tied to the bog and has grown deeply connected to its natural and spiritual dimensions, which is what makes it so difficult for her to leave, even though everyone is urging her to do so. The Bog of Cats symbolizes Hester's connection to her own family, however traumatic her memories may be.
Fishing Knife (Symbol)
The fishing knife is the implement that Hester uses to kill both her brother Joseph and her daughter Josie. In many ways, it symbolizes her violent and unpredictable side, the fact that she is capable of dark and horrible acts.