The Ghost House is a location found in games in the Super Mario series, first introduced in Super Mario World for the Super Nintendo Entertainment System. A ghost house is shown as an old wooden building, that looks like a typical "haunted house", and which is full of ghosts of various types. Since Super Mario World was introduced in 1992, the Ghost House has appeared in many different games, including games where it makes less sense (such as in the Mario Kart racing games).
To put the Ghost House into perspective, it is necessary to give a brief recap of the Mario series. The first Mario game, Donkey Kong, took place on a single screen. The first true Mario game involved movement and exploration, but it was linear: you moved from left to right. The next two games introduced non-linear exploration and puzzle solving. The third game actually introduced the ghost enemy Boo, but he was just in a "fortress". In general, the technical limitations of the original NES, with its simple palette of bright colors and limited memory space, kept most games simple and linear.
The Super Nintendo Entertainment System expanded the technical range of games. With its wider color palette, its graphics were slightly less cartoony, and it also allowed transparency effects that could portray fog. Also, Nintendo was very successful and had a captive audience, and no longer needed to cater to linear, kinetic game play. Thus, the Ghost House: a level full of ghosts, transparent effects, and with the player needing to solve a series of puzzles to succeed. The usage of a supernatural motif was not purely just graphical: with its shifting platforms, appearing and disappearing enemies that appeared to be hunting the player, and constant sense of being lost, it did present some psychological suspense to the player, more so than the normal brightly-lit levels where Mario jumps fantastic distances. Indeed, if we wish to follow in the footsteps of those who have analyzed Mario, we could read a lot into Mario's attempts to find a key to fit into a hidden lock or his quest to uncover a secret door, all while being pursued by amorphous blobs of ectoplasm.
That being said, while the presence of the Ghost House does widen the game play and atmosphere of the Mario games, Mario is still a bright, happy, fun, and almost plotless game series designed for all ages of video gamers: I have never heard anyone say that a Ghost House level's ghosts were so scary that they couldn't play. The Mario games are many things, but horror is not one of them.