This is a simplified version and much more extensive information can be found. There are two major issues this is meant to address: why we need your logo as vector art, and to help you understand our choice in X format.

Raster

Artwork is being represented by pixels. If a file is 500 pixels square, and you blow it up to 2000 pixels, it will lose quality because the information is not there. You can do it anyway, and that's called "interpolation", but for the most part, that's not a good idea. Raster images really shouldn't be scaled too much.

Common file formats: .jpg .gif .psd .tif .bmp .pdf*

Common uses: photos and most images saved for the web (Flash can use vector artwork though)

Vector

Artwork that is made up of points, lines, and curves. This can be scaled infinitely; it is resolution independent. Logos really should be vector except in extremely isolated instances.

Common file formats: .ai .eps** .pdf*

Common uses: logos, a lot of drawings, architectural plans, type, etc. Except for photos, nine times out of ten, vector is probably a better choice

*PDF: A PDF has the best of both worlds. What is raster remains raster and the vector remains vector (once again, this is a very generalized explanation). This is why a lot of the files we provide are PDFs.

**EPS: Once upon a time, the .eps was the default vector format. This is long past, but it created a lot of bad habits with vendors who expect all files to continue to be presented as .eps. An .eps can be vector, but isn't necessarily vector. You can take a .tif and resave it as an .eps, for instance. In fact, you used to have to do this for duotones. But that doesn't make the artwork vector. That is why we specify "a vector .eps", instead of just "an .eps".