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; Bonnie Bennett, Vicki Donovan and Lexi Branson 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 ghost, they will still possess their werewolf powers.
Witch Abilities: If a witch becomes a ghost, they will still possess their magic as a ghost. It has been shown numerous time that witches can still perform feats of magic while on the Other Side as spirits. Such as the burial ground witches, they performed magic by channeling their own death spot. However it has been shown that powerful witches can directly affect change through the use of their personal Talismans, such as Esther Mikaelson in Ghost World. Witch spirits are also capable of using their powers as seen in Graduation when made manifest; this was only made possible because Bonnie hadn't put the veil back up.
Hunter Abilities: If a Supernatural Hunter becomes a ghost, 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 ghost, 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 was 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 go to the Other Side, instead of the peaceful human afterlife.
Spirits on the Other Side could, during moments where the Veil was down, manifest themselves as Ghosts. They were able to interact, and cause harm, to those on the physical plane.
After the destruction of the the Other Side, the spirits were transported to various other dimensions that remain unknown.
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.
There are several ways in which a ghost is able to gain a foothold on the physical world:
Manifestation spell - to reveal veiled matter
Lifting the Veil - essentially resurrecting spirits back on to the mortal plane.
Unraveling of the Other Side - Physical Interaction with the mortal world though unseen to all except mediums and possibly witches.
The ghosts of deceased witches known as The Spirits and are the only types of ghosts that are not bound to solitary and 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.
Before the destruction of the Other Side, at least two ghosts were able to find peace Sheila and Lexi. Conversely, several ghosts were sucked into a still-unknown dark void; Silas, Markos, Maria, and Vicki. It is unknown if this is the same dark void where Katherine Pierce went after her death, though it appears as such.
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 to 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 Ancestral Spirits.
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.
Witches have the power to transport spirits into other bodies.
In Ashes to Ashes, it was shown that the witches, Dahlia and Esther found peace upon their deaths. Even though they were considered to be two of the most powerful Dark Witches and went against Nature for their use of Immortality spells and the creation of vampires, forgiveness and peace could still be found.