There are essentially two types of images: raster, and vector. Most images are raster; these are bitmapped images based on pixels (jpgs, gifs, etc are all raster). Vector images are based on formulas. The advantage of this is that they can be expanded or shrunk to any size without losing any quality.
Photoshop is built for doing raster imaging, while Illustrator is built for vectors. There is some vector stuff in photoshop though that works well enough for some things - the pen tool. Google a tutorial on it, it's fairly easy to get the hang of (for tracings, at least).