3D Printing is a process whereby a 3D design is turned into a real object. First, software is used to slice the 3D design into layers, and then the design is printed layer by layer on a 3D printer. Because each object is built up uniquely, 3D Printing is great if you want to make unique and customized items or small series of objects. In contrast, other processes, such as injection molding are much better at making thousands or millions of copies of something cheaply.
The technical term for 3D printing is Additive Manufacturing. However, the public almost exclusively uses the term 3D Printing.