Dimensions define the space that an object can exist in. Imagine a fine line; this has only one dimension, length. If you add a second dimension, width, you have a 2D or two-dimensional space. 2D or two-dimensional shapes have length and width but no depth. They are flat, like a comic strip or a drawing. Circles, squares, triangles, rectangles -- these are all two-dimensional figures.
A 2D graph has two axes, generally called X and Y. Most drawings, photographs, paintings and standard picture books are all two-dimensional. 2D animations are flat; although the impression of depth can be created in some elements using light and shading, this is usually restricted to the background. Cartoons like "Scooby-Doo" and "The Flintstones" are examples of 2D animation. Standard movies are 2D; there is some impression of depth because they are recorded in the real world, but the image on the screen appears flat.
2D spaces have height and width. If you add a third dimension, depth, you have a 3D or three-dimensional space. 3D or three-dimensional shapes have depth as well as length and breadth. Pyramids, cubes, spheres and cylinders are examples of three-dimensional shapes, as opposed to two-dimensional triangles, squares and circles.
Three-dimensional graphs allow three axes instead of the more usual two. A sculpture is an example of a three-dimensional model. In contrast to an ordinary picture-book, a pop-up book has three dimensions. In animation, 3D means that elements are constructed so that they appear to have depth; examples include feature-length animations like "Who Framed Roger Rabbit," "Shreck" or "Wall-E." In cinema and TV technology, 3D refers to techniques that make the picture appear to have depth. Typically you need to view 3D TV and movies through special glasses to see the effect. (See References 5)
The terms "2D" or "two-dimensional" can be used metaphorically to mean a work or element of a work that lacks substance, nuance or sufficient thought. A character in fiction who is badly written and lacks personality may be described as two-dimensional or, more informally, 2D. An over-simple system or approach to a problem can also be described as two-dimensional.
The terms "3D" or "three-dimensional" can be used to describe a system, approach or work that is sophisticated, thorough and in-depth. A three-dimensional character in a book or movie is believable and realistic. A three-dimensional approach to something takes in all the important factors instead of focusing narrowly on just one or two.