Vector graphics use mathematic equations to determine the positions of lines, points, curves etc in relation to each other and then save these equations within the file.This means that when you increase the size of the image, the program uses the equations to recalculate the best position to place the pixels to give you the best image possible.Vector graphics are useful when you need to make images which will have their size manipulated depending on the use. One example would be a company logo which will be used in a range of sizes (small for letterhead, medium for front cover of a pamphlet, and large for advertising. You can save one file, and rescaling will not lose quality or proportions.For a broader description see linked source below
