Dementors (Symbol)
Dementors symbolize death, which is a continuing motif throughout the series. The book opens with Harry fighting off a Dementor that attacked him and his cousin. This attack, in a Muggle neighborhood, raises some suspicions, which symbolizes the change in the tone of the novel with Voldemort's "rebirth."
Thestrals (Symbol)
These creatures are only visible to people who have seen death. When Harry sees them he is concerned because the only other person who can see them is Luna Lovegood, whom the other students call "Loony Lovegood." She explains to Harry that she can see them because she saw her mother die in front of her. Since only certain people can see Thestrals, they symbolize death in the Wizarding World. Luna expresses to Harry that they are very gentle creatures and they only have a bad reputation because of who can see them.
The Veil (Symbol)
The veil in the Department of Mysteries symbolizes the threshold between life and the afterlife. Harry hears voices emanating from inside the veil, and he's fixated by the temptation to step through it and join the voices. Later in the book, when he and Luna are discussing lost loved ones, Luna assures Harry that they'll meet their lost loved ones again someday and that their spirits live on in another plane. The veil is a physical manifestation of her faith. Ironically, the veil complicates the very idea of faith, which is belief in the absence of proof, because the veil offers tangible evidence of the afterlife.
The Black Family Tapestry (Symbol)
The family tapestry is obviously a prized possession of those witches and wizards who believe in the significance of their pure-blood status. To them, it reinforces that they are better than those witches and wizards with Muggles in their lineage. When Harry is at Grimmauld Place with Sirius, the Weasleys, and other Order members, they come across the Black family tapestry. Harry looks and is unable to find Sirius, who has been "blasted off" by his mother after running away. The tapestry is a symbol which demonstrates the divide in the Wizarding World over blood status. Sirius ran away from home to escape his parent's "pure-blood mania" and his parents removed him from the family.
The Room of Requirement (Symbol)
The Room of Requirement is another symbol of faith in The Order of the Phoenix. The Room is the embodiment of the idea that if one believes in something or needs something badly enough, it will simply materialize before them. A running theme of the series is that help and aid will always be furnished to a person whose intentions are good and true, and the Room of Requirement is another tool to that end. The Room also reinforces the idea that Hogwarts Castle is a living, responsive being that supports its inhabitants and aids them in the ultimate goal to conquer "evil," as is evident is smaller ways, like Dumbledore's office sealing itself against Umbridge even after she's named Headmistress.