Is the printer you use regularly right by your side (or at least in the same room) or is it down the hall and shared with a dozen others? That's one of the differences between a local printer and a network printer. When doing desktop publishing, a local printer is convenient. But a network printer has certain conveniences as well. In an office setting, multiple people can share a single printer and at home, a printer on your home network means you can print from the your home office, your living room, your kitchen, or even your front porch without physically lugging the printer around with you. And other family members can use that printer too.
The same is true when the printer you're talking about is a printer service rather than a piece of hardware that communicates with your desktop computer or laptop.
Online Printing vs. Local Printing, an article by Charen Smith lists pros and cons of each option. Shipping costs are one of the issues you must consider when choosing to have your printing job done at some faraway location.
Keep It Local - The Benefits of Using a Local Print Shop from graphic designer Laura Vatalaro outlines many reasons why you might want to deal with a local print shop and disputes the oft-repeated suggestion than online printers can give you better pricing on your desktop publishing projects.