There are two basic methods used by computers to store graphic image data: raster and vector.
Raster (or "bitmapped") images store rows of data that represent the color and intensity values of consecutive "dots" (or pixels) that make up the image. Common graphic formats for raster images are GIF, BMP, JPEG, PNG and TIFF. Cameras and scanners almost always generate raster images.
Vector images describe pictures by storing shapes in terms of their point positions, connecting lines, curves and color. You can think of it as a mathematical description of the picture. Common graphic formats for vector images are WMF, EPS, and SVG.
Metafile formats such as PSD and CDR store both raster and vector data.
Since vector images use mathematical relationships to describe the picture, they scale in size very well. The image always looks smooth regardless of the size. When raster images are resized larger, the dots get "fatter" and occupy more pixels on your display. This results in a chunkier image (the "jaggies").
Photoshop is a raster-based image editor, although it does use some vector data for things like "shapes" and fonts. Adobe Illustrator is primarily a vector-based image editor.