What is the difference between 2D and 3D animations?

To that excellent, succinct, answer, I'd add that 2D tends to look "flatter" than 3D (due to the natural limitations of the horizontal and vertical planes). As Joe-Speedy says, 3D introduces "depth perspective," so we not only see a rectangle (2D) but a CUBE (3D). You may want to think of it like being the difference between a photograph of a glass of water (2D) and being able to reach out and actually pick up the glass of water (3D). Another good visual might be comparing a cartoon (say, Bugs Bunny - 2D) to "Toy Story 1,2 & 3" (3D). Typically, 2D involves "drawing," or movement on, say, a flat surface (sketch pad, etc.) or in the vertical and horizontal planes. 3D involves "modeling," i.e., creating objects in 3-dimensions, residing in an expansive virtual environment, replete with lights, reflections, other objects, shadows, etc.

2D and 3D refer to the actual dimensions in a computer's workspace. 2D is 'flat', using the X & Y (horizontal and vertical) axis', the image has only two dimensions and if turned to the side.
Animations in 2D involve manipulations on a graphics "surface", where animations are rendered pixel-by-pixel onto a graphics memory area that corresponds to the viewing space allowed by the graphics.


2D is an image drawn in the X, and Y dimensions. 3D is an image drawn in the X, Y, and Z dimensions, however most often what is referred to as 3D is a 2D simulation of 3D.