I had a buddy that had this question recently. I think this is a great explanation…
For print production (and web, actually) there are two basic image types: raster and vector. Raster images are made of pixels. Vector images are made of lines in the geometry sense of the word: they don’t have a thickness, really. They’re algebraic equations.
This is a sample of a raster image:

Raster images are resolution-dependent. They’re only as good as the resolution they were created in. The more resolution, the better, to start with. You can always go down, but you can’t really go up without cheating, and cheating only gets us so far. (That’s why you want to buy the highest-resolution stock photography when you buy it, in the event you have to do a poster or something.) Materials printed with raster images are limited in quality on the low end by the resolution of the file, and on the high end by the resolution of the output device. So if your press only gets 300dpi resolution, it doesn’t make any difference if your file is 3,000dpi resolution. If your file is only 72dpi resolution, however, it will look awful on that same press. Photos are raster images. File types: JPG, GIF, BMP, TIF, STX, PSD, EPS*
This is an example of an outline preview of a vector image (as represented on my monitor, which is, alas, raster):

Vector images, because they exist as equations, can always be scaled up. Those lines you see are simply the computer saying that there exists a boundary with location (2, 4) to (2, 8.34) or whatever. They are resolution-independent. You can take the same file that’s used on a business card and use it to cover a billboard. The resolution of a vector image is only limited by the resolution of the output device. Except for photos, vector images are almost universally preferable to raster images.
Type is vector-based. It exists in a type format (OpenType, TrueType, PostScript), and is editable and searchable as type until it is converted into pure outlines (which is what you see above). Once that’s done, you can edit the type as artwork — it might as well be a circle or a triangle — but you can’t edit it as type.
When you convert from raster to vector, you have a fully scalable, albeit rough approximation, of the original vector art. When you convert from vector to raster, you get a bloody mess, which is what we have in the top image.
Vector file types: AI, FHD, SWF, PDF, CAD, EPS*
*EPS and PDF files are similar. PDF files are essentially EPS files with a type of compression encoding. EPS stands for Encapsulated PostScript. It’s really a language with a file type associated with it. The language describes objects on a “page” for the use of output devices. That’s why raster images can be EPS files.
Some designers name their raster images with a .EPS extension. This is a bad idea, unless there’s a specific use for that file, like using a vector path embedded in the raster file to create the illusion of a transparent background (known as clipping). Because of that bad habit, there’s often some confusion as to what is meant by “Send me an EPS file.” It really means, “Send me a vector-based EPS file.”
Pass it on to your newbies… Enjoy!
Best,
Murray