As cleverly explained in the book Flatland by Edwin Abbott, reality is made by many dimensions, and depending on your perception skills, you can see and act only on some of them. This is true also in video games: video games can be set in 3D or 2D worlds, and this distinction determines the way in which agents can perceive the surrounding world and so their ability to move and act.
An N-dimensional space is a geometrical setting in which a point in space is identified by N values or parameters, commonly named after the last letters of the alphabet.