Illustrator is the complementary software to Photoshop. Photoshop/PSP/GIMP are for editing bitmap/raster graphics: photographs, paintings, and the like where individual pixels are the important thing.
Illustrator and most CAD programs use vector graphics. Instead of the pictures being composed of pixels, it's composed of lines and curves which have certain characteristics. When you magnify raster graphics by a factor of ten, you have huge pixels; when you magnify vector graphics, you have the same lines you had before.
Vector graphics are generally used for (as mentioned before) CAD projects, corporate logos, maps--anywhere where scalability is more important than absolute size.