What ON EARTH is a vector graphic file? Does it have anything to do with angles or angels? Was it named after a guy named Victor, then over the years was it mangled into the word "vector" by laymen with an eye for verbal destruction and a desire to see the English language burn? Is Vector a town in Minnesota where they milk moose to make cheese, which they then mark up at ridiculous prices to sell under the ever-so-classy moniker "Moose Cheese By Vector?"
According to Wiki, this is what a vector graphic file is:
Vector graphics is the use of geometric primitives such as points, lines, curves, and shapes or polygon (s), which are all based on mathematical expressions, to represent images in computer graphics. Vector graphics are based on vectors (also called paths, or strokes) which lead through locations called control points.
Oh my goodness, gracious, I've got a headache.
Basically, a vector graphic is a scalable art file made in a program such as Adobe Illustrator. These files typically end in one of the following extensions: .ai, .eps, .ps, .svg or .pdf. Instead of an image being made up of a ton of pixels laid out and plotted forever in their unique spots, a vector graphic stores the information on the location of many points (anchors) so that your graphic can be made larger or smaller without losing any image clarity at all. You can zoom in to your graphic until you're so close, you'd be able to see bacteria in real life. And even at this close level, there are no blurry pixels. Instead, you see the same number of pixels as you saw when zoomed out, only re-organized to sharply portray a tiny point on your overall graphic.
Why is this important to you or your printer? It allows for re-sizing your awesome designs without losing any clarity at all. You can take a graphic that is normally ten inches across and re-size it to fit on a half inch wristband, or vice versa. Without a vector file, such drastic changes in sizing would result in image quality loss that could seriously hurt the end product.
When you see a poster on a wall that is 10 feet wide and 10 feet long, the artist did not have to create an awful art file in order to print the massive image. All he / she had to do was create a vector file of any size (12 "x 12" for example) and the printer was then able to blow up the design until it was a big, humongous advertising masterpiece.
Think you've got it? I hope so! Good luck vectoring, my friends.