Bitmaps are made up of pixels, while vector images are composed of mathematical formulas that consist of curves and points. As such, they can be resized at will without losing quality. Making a bitmap larger makes the pixels larger too and the result can be blurry and jagged. Photos are bitmap images, and so are file formats like bmp, jpg, and psd. Illustrator files are vector, and well suited to drawings and illustrations.
In the illustration shown here you see two hibiscus flowers. The one on the left is a photo, and is a bitmap. The one on the right is a vector illustration. It's one of the symbols from the Flowers symbols that comes with Illustrator CS 2.