Marshy has got it right. We had prototypes of a plastic housing done this way quite a few years ago when it was referred to a rapid prototyping - 3D printing is partly a new name and some hype, but there is also a lot of technology advancement going on. You first make a drawing in a 3D CAD software package - we're using AutoDesk Inventor, which is quite expensive and takes a while to learn. Drawings typically start with a series of 2D "sketches", which are really traditional 2D CAD drawings of lines, arcs, circles, etc., and then these are turned into 3D shapes by extruding, revolving, etc.
When the 3D drawing is done, you export the file in a particular defined format (.STL). Next that file is run through a program called a "slicer", which converts into 'G-codes", which is mostly XYZ coordinates in a format similar to what is used with numerically controlled machine tools. More importantly this is where you set up whether it will will be solid or hollow, what fill level and pattern will be used, what surface resolution is used (which is mostly the Z-axis print speed, as the string width is fixed), and create any support structure needed.
Then the G-codes are sent the printer, which has a heated extruder head - basically a heated tube with a gear mechanism to push the plastic string through it - run by servo motors and screws that can move it around to precise locations. Then it draws the part by layering thin (0.4mm) strings of hot plastic upon a flat surface.
There are many limitations in the characteristics of the materials, the resolution of the part features and the surface finish, and the need to print a support structure under overhanging features, which must then be cut away.
The majority of 3D printers use thermoplastic string that looks like a roll of string trimmer line. There are a couple of common materials available; PLA (plant based), PETG, ABS and others. The surface quality is poor and it is very slow. However, it is still a useful tool - we got one to make prototype parts, but more importantly to make production fixtures and tooling. There are many of these that do not need to be made of harder materials, and it gets away from the need to design something so that it can be fixtured and milled. I can make other kinds of shapes now.
The whole issue of scanning is something I have not explored - they are expensive and have many limitations.