Have you ever received a print project, anything from business cards to document folders, opened the box to check out the finished product and been disappointed because your logo looks like crap? That's what happens when your printer or promotional merchandise supplier doesn't use vector art or a high resolution bitmap.
You probably have no idea what vector art is, but if you ever buy print or promotional items for your company you should, understanding vector art will save you time, money and headaches.
Vector art is high resolution art work made up of paths which are defined by lines, points and curves represented by mathematical equations. Vector artwork or images can be decreased or increased in size while retaining their sharpness and detail without compromising quality. Vector images usually require less memory and a smaller file size, it is the standard format for corporate logos or illustrations and typography.
Always use vector images for any kind of printing or promotional products that have illustrations or images with type incorporated. If you don't use vector artwork and instead use another format called Bitmap, which is the standard format for JPEG images, TIFF images, GIF images, and PNG images, make sure it's at least 300 DPI to ensure the finished product doesn't come out looking, well, like crap.
This is the primary reason you can't pull a logo or some other image off a website and use it as the artwork for a print or promotional project. Website images are low resolution images with a DPI (dots per inch) of 72 which is fine if you're viewing it on a computer screen but to print that same image you need a resolution of at least 300 DPI (dots per inch).
The other critical thing about vector artwork is that it can be re sized without impacting the quality of the image, this is key for print projects as you often have to re size images to place them where you want them. Check out the images below for an example.
This one uses vector art and you can see that the quality remains consistent even as the size of the image is reduced or enlarged. 
This next image doesn't use vector art, instead it uses the Bitmap format and as you can clearly see the larger we make the image the fuzzier and less distinct it becomes. 
How can this information save you time, money and headaches? When you come up with a logo design or have a graphic artist create artwork for you, make sure when the project is complete you get all the artwork in both formats, vector art and a high resolulution bitmap. This ensures you have the right format for whichever use you choose, on line to be viewed on a screen or off line to be viewed in print or on promotional merchandise.
You'll need both formats anytime you're working on a marketing project whether it's updating your website or producing a printed desk pad calendar as a gift to clients and prospects. When you have all the artwork you need in the correct formats you simply send it off the the appropriate vendor. If you don't have vector art for your printing projects you're stuck trying to recreate it, find it, or chasing after the artist that originally created it, either way it's costly, time consuming, and a headache, all of which you can do without.