So the Dot character was made using 3D printing.  That is achieved by taking model information stored in a 3D modeling program and turning into a real 3D model that can be held and used.  The principle application of this kind of kit lies in the design and engineering worlds where there is a  requirement for prototypes.  With the increasing accessibility of 3D modeling programs such as Maya, Mudbox and the opensource Blender the uses and applications are likely to increase.  

The variety of uses of to which the 3D printing know how can be seen at the Shapeways website.   They can take your design and print it for you at a quite reasonable price. Alternatively you can choose from a range of other designers work.
Below is their 'how its done video'. 



Products available their include Lightpoem for LED candle,  Message Cuff Medium

or this cute fellow  Hoodie 5cm

If you look at these items you can see they are actually printed with a couple of different materials.