Spoiler alert: I'm not going to give away everything here, but if you think revealing the "man behind the curtain" would in any way diminish your future enjoyment of the Haunted Mansion, by all means click to something else.
Many of the attraction's best features are based on age-old magic illusions. They say a magician never reveals his secrets, but in 2003 Disney published "The Haunted Mansion: From the Magic Kingdom to the Movies," by Imagineer Jason Surrell. The behind-the-screams revelations below are largely based on info from the book. If you are interested in learning additional secrets as well as a thorough history and overview of the classic ride, I'd highly recommend the wonderful book.
The Grand Hall
One of the Haunted Mansion's most head-scratching illusions is actually one of the least sophisticated. In the Grand Hall scene, ghosts fade in and out of view as they dine at a long banquet table and dance around a pipe organ. Startling in its realism, the illusion is based on the Pepper's Ghost effect named after the chemist that invented it in 1862. The props in the room are real; the ghosts are images of animatronic characters reflected in the glass in front of the scene. When guests ride by in their Doom Buggies, both the reflected images and the room visible through the glass merge into one scene. Universal Studios Florida used a much larger version of this effect for its Ghostbusters stage show (which has since closed).
The Seance Circle
Madame Leota, the disembodied spirit in the crystal ball, is also a relatively simple, yet wildly effective illusion. Inside the ball is a three-dimensional bust of Leota. Projected onto the white bust are brief filmed sequences of Leota reciting her incantations. When viewed together, the effect is quite astonishing. The same concept is used to animate the singing statuary in the Graveyard scene and the tiny ghost that bids farewell at the very end of the attraction.
The Hitchhiking Ghosts
It's a similar Pepper's Ghost illusion, but this time the ghosts are behind the glass and the guests are reflected in the mirror.