Computer graphics help (Vector files)!

My dad is doing some artwork for someone, and he needs to convert his drawing to a "Vector" file. Is this like a jpg, gif, or bmp file?

The graphics program we have on our computer will convert a picture to any of the "common" files listed above, but we don't know what a "vector file" is. My dad said it can be done on a program called "Adobe Illustrator", but it's a pretty expensive program. Also, would it be possible to just scan a hand-drawing, and then open it in a program to a vector file?

Any more info would be great. Thanks in advance!

Here's a link describing what a vector is.. (I'm too lazy :p )
http://searchwebservices.techtarget....213284,00.html

I use Flash MX to make vector images or to convert an image to a vector...