There are two definitions of Two-and-a-half-dimensional, or 2.5D, perspective:
The initial usage of the term Two-and-a-half-dimensional was to describe games that were not displaying "true 3D" graphics. Instead, these games relied on mathematical calculations to simulate 3D by rotating or scaling 2D sprites or textures to simulate a 3D effect.
Examples of Pseudo 3D
2D game with 3D graphics
In 1997, Sega released Clockwork Knight, a platforming game is one that uses 3-D rendering techniques, but restricts the player on a set path, similar to a 2-D game. Since then, the term Two-and-a-half-dimensional have been used to describe games with 3D graphics but is designed with the restriction of a 2D game.