If p is any plot object, then you can use the save method to save it to a file. The type of file written will be based on the extension of filename given. For example,
p = plot(x^2, -5, 5)

will save an SVG. Since the directory in which to save the image was not specified, it will do it in a special directory reserved for the input cell. The notebook will automatically detect that this file is present and then either display it or display a link from which you can download it. You can also use .eps or .ps for PostScript files which are also vector graphics.