So you are wondering what a 3D printer actually is?
Well, basically, a 3D printer is just like a normal printer, only ... it uses plastic to print, and it prints layers of plastic on top of eachother. These layers then form the object you want.
Having a 3D printer in your house will really change things. No longer to you need to get a new cup if your other broke, you can just print it! Other fine examples of things you can print are vases, chess pieces .. too much to mention. Check out http://www.thingiverse.com for some great examples!
This picture found on the internet is the best explanation possible of what a 3D printer will do for you. And since a picture says more than a thousand words, what better way is there than to just show it?