3Dprintingindustry.com has a wonderful 3D Printing Basics: The Free Beginner's Guide which provides an overview of 3D printing. It includes a brief history of the technology, the processes and materials used, and applications. The type of 3D printing highlighted below pertains to Joyner Library's 3D printers, but there is much, much more to learn!
3D printers (e.g., Makerbot, FlashForge, Printrbot, Ultimaker, etc.) that use FDM, also known as Fused Filament Fabrication, build objects layer by layer from the bottom up. They do this by heating plastic filament and extruding it through a small nozzle onto a build plate. Before printing, special software "slices" the 3D model into layers and calculates, or maps, the the X, Y and Z coordinates the printer's extruder will travel to build each layer.
After each thin layer (~0.2mm) of plastic is extruded, it cools and hardens. As it cools the plastic binds to the layer beneath it, and the build plate is lowered so a new layer can be added. Printing time depends on the size and complexity of the 3D model being printed. Small objects can be printed rather quickly, 30 minutes or less, while larger, more complex objects can take many hours.
FDM is arguably the most popular type of 3D printing and is most often used by hobbyists and other non-commercial enthusiasts. Although, commercial businesses are known to use FDM for new product development, prototyping and even in manufacturing development. This technology is considered to be simple-to-use and environment-friendly.
You can visit additively.com to learn more about 3D Printing, and Fused Deposition Modeling. Stratasys has also produced a video showing details of the FDM process. Here is a recent article on Digital Trends about the difference between ABS and PLA filaments.