A picture that has or appears to have height, width and depth is three-dimensional (or 3-D). A picture that has height and width but no depth is two-dimensional (or 2-D). Some pictures are 2-D on purpose. Think about the international symbols that indicate which door leads to a restroom, for example. The symbols are designed so that you can recognize them at a glance. That’s why they use only the most basic shapes. Additional information on the symbols might try to tell you what sort of clothes the little man or woman is wearing, the color of their hair, whether they get to the gym on a regular basis, and so on, but all of that extra information would tend to make it take longer for you to get the basic information out of the symbol: which restroom is which. That's one of the basic differences between how 2-D and 3-D graphics are used: 2-D graphics are good at communicating something simple, very quickly. 3-D graphics tell a more complicated story, but have to carry much more information to do it.
For example, triangles have three lines and three angles -- all that's needed to tell the story of a triangle. A pyramid, however is a 3-D structure with four triangular sides. Note that it takes five lines and six angles to tell the story of a pyramid -- nearly twice the information required to tell the story of a triangle.
For hundreds of years, artists have known some of the tricks that can make a flat, 2-D painting look like a window into the real, 3-D world. You can see some of these on a photograph that you might scan and view on your computer monitor: Objects appear smaller when they're farther away; when objects close to the camera are in focus, objects farther away are fuzzy; colors tend to be less vibrant as they move farther away. When we talk about 3-D graphics on computers today, though, we're not talking about still photographs -- we're talking about pictures that move.
If making a 2-D picture into a 3-D image requires adding a lot of information, then the step from a 3-D still picture to images that move realistically requires far more. Part of the problem is that we’ve gotten spoiled. We expect a high degree of realism in everything we see. In the mid-1970s, a game like "Pong" could impress people with its on-screen graphics. Today, we compare game screens to DVD movies, and want the games to be as smooth and detailed as what we see in the movie theater. That poses a challenge for 3-D graphics on PCs, Macintoshes, and, increasingly, game consoles like the Dreamcast and the Playstation II.