Vector graphics are sometimes also referred to as "draw graphics," but they mean the same thing. The technical definition of vector graphics is complicated, but in a nutshell vector files are a type of graphic that uses mathematical algorithms, allowing the image to be scaled or modified without loss of image quality or resolution. These images are easy to resize or rescale and result in a better quality graphic!
When you create an image in Adobe Illustrator (or in Freehand or CorelDRAW), you are creating a vector graphic. However, when you create an image in a program like Adobe Photoshop, you are creating a bitmap graphic, which is not a vectored format. A vector graphic retains its crispness at any magnification, but a bitmap graphic appears jagged when it's enlarged.