vector vs. raster
Vector graphics are math (lines and curves between points) and scale infinitely without quality loss. Raster graphics are pixels and degrade when enlarged. Logos should be vector; photos are always raster.
Common vector file formats: SVG, AI, EPS, PDF (when saved with vector preservation). Common raster formats: PNG, JPEG, GIF, TIFF. For print, logos and icons should be supplied as vector — they'll print crisp at any size from a business card to a banner. Photographs are inherently raster (they capture pixels of light) and must be supplied at sufficient resolution for the final printed size. A common mistake: copying a logo from a website (always raster, low-DPI) and printing it large — it will look terrible. Always source the vector original.