3D printing is the process that makes physical objects from virtual CAD models.  There are many different ways to do it, but they all work by building up models one layer at a time.  It's not a carving process: computer-controlled mills can be used to cut a design out of a solid block of material, but that method doesn't work well for designs which have a lot of undercutting, like mine.

There's a huge variety of 3D printing processes available, all using different materials in different ways, and mostly proprietary to competing companies.  I won't try to survey the field here (The Worldwide Rapid Prototyping Directory does a great job) but as an example I'll describe the Solidscape Modelmaker II, since I've operated it.

This machine uses wax as its material, and it prints very small high-resolution models which are mostly used for making jewelry.  Overall it looks like a Xerox copier from the 1970's: chest-high, beige plastic, and it hums except when it's doing something louder.  It works something like an inkjet printer, and something like a pen plotter.  There's a pair of heads mounted on rails so they can move in the X and Y directions, and each head contains a jet that shoots wax drops instead of ink.  And the table over which the heads move can go up and down in the Z direction, so that each layer can be printed on top of the last.

Above, looking into a Solidscape machine at work.  The pink and green jets in the center are shooting drops of the two materials onto the model.

The green head shoots "build" wax, which is the green material that the models are made of, and the pink head shoots "support" wax. This softer material encases the model as it is built, and fills in all interior spaces and overhangs. After the build, it is removed by soaking in a solvent.

Digital image of a pair of parts ready to be built.

Screen shot of a toolpath: this is a layer near the bottom.  Build material is green, and support is pink.

A layer farther up, in the middle of the piece.  This shows how the support material fills the large central void in this model, which would otherwise sag or collapse during the build.

Finished wax models: the pink support material has been dissolved away in a bath of hot solvent, leaving only the green wax.

This Solidscape machine is fairly typical in how it builds up models out of layers.  It's unusual in that it uses wax -- it's one of very few processes that can produce a burnable model -- and in its small scale: it has excellent resolution, but is only useful up to about 1" in size.  This is the type of object I used to make with it:

A 1 1/4" silver piece, cast and polished from a Solidscape wax model.

Another type of 3D printing that I've used is Z Corporation's process, which builds rough-grained models from cornstarch or plaster materials.  ZCorp starch models can be used with lost-wax casting, and I made a number of bronzes that way, but it is quite labor-intensive, and I'm just as happy not to be doing it now.

At present I'm using direct-metal printing by Ex One, which is a much easier way to produce metal sculpture, and well suited to my work.  The lamps which Materialise is printing from my designs represent yet a fourth technology, this one producing a durable white plastic.

I've barely scratched the surface of this field -- I haven't even mentioned the commonest process of all, stereolithography -- but you can see there's a lot to learn: many technologies, all doing different things, and it can take careful study to figure out which is best for a given project.  But I can say that the art on this site gives a good sample of what 3D printing is best at: making things that are too complex and undercut to even think about with casting.