Ghosts are a race of undead beings; more specifically, the returning spirits of people with unfinished business.
Only Psychics, such as Ethan Morgan, can see ghosts. They are intangable, and as such can't be harmed by physical force (although Ethan was able to touch Olivia in her mirror, this was presumably only because they were both trapped in a ghost realm). They can be affected by magic; some spells harm them, and it is also possible to exorcise a ghost, but this does not always work, expecially against stronger ghosts.
Ghosts can be somewhat indestructible, to an extent. They have abilities such as telekinesis, future-seeing, face-morphing, and teleportation. They can also cling themselves onto objects of significant importance to their former lives, and some stronger ones, can even posses greater powers, such as being able to possess others.
Apparently, vampires can also have ghosts, despite the fact that they are already dead.
Coach Ed - The first ghost to have appeared in the series, appearing in the episode "Friday Night Frights". He made his first appearance when he was released from Whitechapel High's only trophy. Although only seen by Ethan, Ed nonetheless wanted the 'nerd' to win him a new reward, blackmailing him by torture until he gave in. He was ultimately forced by other, unseen spirits into passing over into his other life.
Jacob - A mechanic who made Manfrien Bruner's car, Jacob later began life as a vampire, and as such was fired. In vengeance, he stole the car, but was killed after having an accident and falling into a wooden fence, his spirit latching onto the car in the refusal of passing on without killing all of Bruner's relatives. With this in mind, he continually murdered all of his former employer's family until he eventually stopped, presumably having run out of family members. Years later, when Ethan touched the car, his psychic energy awoke the ghost, who continued to attack Bruner's desendants. He was defeated, however, when Ethan flipped the car, and Sarah stabbed it with a giant stake.
Olivia Frye - The star in a school production of "The Rainbow Factory" in 1987, Olivia had obviously been bullied at Whitechapel High, and was tragically crushed onstage after a prank gone wrong by two mean girls who tried to sabotage her performance in front of everyone, as to have originally tried to emberass her. Because of this horrid death, her infuriated spirit was trapped inside of her personal dressing room mirror, where she continually began to semi-posses others (she controlled them, but mostly reamained within the mirror). When the script was found again years later, the vain spirit of the mirror possessed Erica, and sucked Ethan into the opposite side of the mirror. Regardless, she was later stopped after the mirror was cracked by a spell from Benny, and Ethan smashed it. However, having now fully posessed Erica, she tried again to get revenge, but was stopped by the combined efforts of Ethan, Benny and Sarah, being placed within a new mirror that was painted-over so none could look within.