Anna said it's like being here with all of us, only we can't see her or hear her, and she can't interact with anyone. She's all alone.
— Jeremy Gilbert about ghosts.
A Ghost was the soul and spirit of a deceased person that could, under certain circumstances, appear as a visible manifestation to the living, and in even rarer circumstances, physically interact with the living world. However, following the destruction of the Other Side in The Vampire Diaries' episode Home, it is unknown if ghosts can still linger on the earth, or if their spirits move on to one of a number of afterlife dimensions.
Ghosts do not appear any different dead than they did when they were alive. Whenever they appear to the living, they are usually seen dressed in the very same attire they were wearing at the time of their deaths. However, it's possible that ghosts can somehow change their appearance and manifest different clothing. Both Bonnie Bennett and Vicki Donovan were shown wearing different clothing on the Other Side than the outfits they originally died in.
Powers and Abilities
Intangibility: Ghosts cannot physically feel nor can they be physically felt, unless they are given a physical foothold in the land of the living.
Vampire Abilities: If a vampire becomes a spirit, they will still possess their vampire powers. Vampire ghosts are capable of showing their fangs, with Kol Mikaelson being the first to do so.
Werewolf Abilities: If a werewolf becomes a spirit, they will still possess their werewolf powers.
Witch Abilities: If a witch becomes a spirit, they will still possess their witchcraft powers. The ghosts of witches were capable of using their powers in Graduation, but this was only possible because Bonnie hadn't put the veil back up.
Hunter Abilities: If a supernatural hunter becomes a spirit, they will still possess their hunter powers.
Isolation: Ghosts can interact with the living through mediums and witches. However, if the person chooses to isolate themselves from the spirit, they will be forced to vanish.
Magic: Ghosts are susceptible to the forces of witchcraft. Because the other side was destroyed by a magic spell, all the ghosts who couldn't come back to life got sucked into the dark void or found peace.
The Other Side is the mysterious dimension where the spirits of dead supernatural beings reside. It was created by Qetsiyah in an attempt to imprison the immortal Silas. The spell ensured that every supernatural being that died would come to the Other Side, instead of the peaceful human afterlife. After the destruction of the Other Side, the ghosts were transported to various other dimensions that remain unknown.
Oblivion was a mysterious plane/state of being, when The Other Side was imploding and spirits of the Deceased we're sucked there and possibly destroyed.
Qetsiyah was indirectly responsible for the existence of ghosts. By creating the Other Side, she prevented the souls of deceased supernatural beings from finding peace, thus trapping them as ghosts on the Other Side.
According to bonnie, ghosts are also known as Veil Matter.
There are several ways in which a ghost is able to gain a foothold on the physical world:
Manifestation spell - hole from resurrection TBA
Lifting the Veil - TBA
Unraveling of the Other Side = Physical Interaction TBA
The ghosts of deceased witches known as Spirits and are the only types of ghosts that are not bound to solitary can interact with one another and retain their ability to influence the physical world with their magic.
They are a collective force and known to carry out consequences on behalf of Nature before the collapse of the Other Side.
Since the Other Side has been destroyed, it is currently unknown if ghosts can still exist, at least on Earth.
Bonnie Bennett and Damon Salvatore were both ghosts on the Other Side when it finally disintegrated. It is unknown where they went, but it can be assumed it is a different place than the dark void, as they saw a bright white light before they disappeared.
As revealed by Genevieve in A Closer Walk With Thee, ancestral witches are consecrated in the Earth after they die so their power can be used by their descendants. For this reason, they do not go to The Other Side, and instead are a different type of ghost.
Bonnie and Damon are seen in I'll Remember in a kitchen and happily having breakfast together. They were initially believed to be ghosts who found peace.
This was later proven false in Yellow Ledbetter, when it was revealed they were stuck in in a dimensional time-loop of May 10, 1994.