Describes situation between one-dimensional and three-dimensional. See A.K. Dewdney's The Planiverse or Flatland.

Having Length and Width.

The ideal two-dimensional shape is the square, with equal length and width. The shadow, from the top, of such a square is the one-dimensional line.

Possessing width and height, but not depth (the third spatial dimension). "Flat". Often used as part of the phrase "two-dimensional surface", such as a flat painting, tabletop, wall, or floor.

In a literary context, a two-dimensional character is one who possesses ambitions and motives, but no clear past or reasons to explain them. Most TV or comic book characters begin as two-dimensional characters until they've existed long enough to have their past and origins explored by the writers.