When I went through 99Designs to get the logo for Startup Next Door, in my proposal I requested that the designers either provide a vector image or a layered PSD with a large DPI (at least 300). By requesting one of these formats, I can be assured that I can use the image on large-format printing like banners and t-shirts.
A vector image is an image made up of a group of mathematical formulae, with each line and gradient represented in math. By using a mathematical representation, the image can be regenerated on another computer using math. This also means that the image has no height or width, because the image changes in size by setting a scale number. Because the image looks the same in any size, it can be increased in size for a seminar or trade show banner or scaled down for a business card and keep its fidelity. This is the optimal image format for illustrations such as logos. Adobe Illustrator is the most common creator/viewer of these files and the filenames typically have the .ai or .eps extension.
Photoshop images (with .psd extension) are typically composed of layers, and each layer can be independently moved or brought to the foreground or sent to the background. A layered image gives you the flexibility to change elements of the image later (such as fonts, shadows, or other details) and keep the rest of the image the same. When a Photoshop file is created, the artist sets the DPI (dots per inch). The larger the DPI, the larger the image can be printed and still look good. Larger DPI also means larger file sizes.
Hope this helps you getting started with your logo the right way. See more here on CafePress about optimizing for large prints.
Disclaimer: I've been using Photoshop for about 11 years, and am still no expert, although I can create some nice things (like this site). I defer to web design tutorial sites for further info.
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