"vectorizing" is the process of converting a raster image to a vector image.
A raster image, such as a .jpg, uses pixel (individual dots) to create a picture. Blow it up too much and you get a distorted picture and "jaggies" along lines, making the larger image look pretty crappy.
A vector image uses a math equation to draw the lines of a picture, so no matter what size you expand or compress the image, it is always clear and the picture always looks just like the original did.
Hope that helps. And to vectorize an image you'll need a program that deals with vector images like Adobe Illustrator. Look on this board for Frosty's vectorial in the Artwork subforum I think.