The Organ Banshees (not to be confused with the more fearsome Banshees) are several spirits haunting the Haunted Mansion.
The "Banshees" seem to be transparent, white, disembodied heads with wisp-like trails as well as empty black eye-sockets, nostrils and screaming mouths.
Real World Background
The term Banshee used for them is unofficial and is derived from the screaming appearance of the ghosts. In mythology and folklore Banshees are not necessarily undead creatures like ghosts but rather tend to just be malevolent spirits similar to demons or fairies and whoever hears their scream is doomed to die in the near future. However some stories claim that Banshees are the spirits of young women and girls who died of violent deaths.
Haunted Mansion Ride
Outside of the Liberty Square Mansion, carvings of the banshees are shown decorated on an organ carving found on the Composer's crypt, similar to how the emerge from the organ in the Great Hall.
The Organist was stated to appear in one of the stories of the cancelled eighth issue. He would have been the sadistic narrator of the tale of how the Banshees who float out of the organ came to be (according to this continuity, they were a choir of obnoxious children that the Organist lured to their death to have a children choir to compose for).