A 3D printer is, as the the name indicates, a machine that can print in 3D. Where a regular printer prints an image from an image-file, a 3D printer prints a 3D model, typically in plastic, from a 3D file. Almost magically, you can create more or less what you want very easily.
Technology
The most simple 3D printers do not actually print in 3D. Instead, they print a lot of layers in 2D on top of each other to make a three dimensional model. They melt a thread of plastic that is laid on a base plate and then on top of the layers beneath, one by one.
More advanced 3D printers use other technologies. Some lay layers of powder where the "positive part" is sintered by a laser. Others use fluid materials that are cured with light. 3D printing is not longer limited to plastic, either; now it is possible to 3D print in materials such as metal, porcelain or precious metals such as gold or silver.
Advantages of 3D printing
3D print ground breaking for more reasons. Firstly, it is possible to fabricate things that simply would not be possible with traditional methods. Imagine, for instance, a conch. That could never be injection molded but can easily be 3D printed.
Another large advantage with 3D printing is that it does not require any sort of tool to produce a model. That means that there are no start up costs, so the first print is as cheap as the next. That means that you can very quickly go from idea to 3D print, which makes it well suited for prototypes.
Uses of 3D printing
With the many opportunities that 3D printing offer, and to the price that 3D printing has reached there are many uses for 3D printing. Rapid prototyping is maybe the most well known but with the quality of modern 3D printing you can also print spare parts and finished products – without the need of a warehouse. An interesting use is medicine where 3D printing is used to tailor every model to the user. Less life-saving uses are miniatures (scale models, role playing figurines etc.) and jewelry.