A 3D printer can make 3 dimensional objects by using a process called additive manufacturing.
The printer can print out a very thin (typically 0.1mm) layer of plastic onto a flat bed. Once the first layer of plastic is printed the bed drops by 0.1mm and the next thin layer of plastic is printed on top of the first. This process continues until the object is fully printed out.
Even a quite small object can take over 1000 layers of printing to make, but the printer does all the difficult work for you.
You can make things and shapes using a 3D printer that would be very difficult, and in some cases impossible, to make in any other way.