There is no MATLAB function that can permit you to download arbitrary images when you do not know of a location for the image.
In the case where you know the location of the image:
Since R2006b or so, urlwrite() has been able to download from URL and save to disk.
Since R2013a and possibly earlier, imread() has been able to read images from URL into memory (and you could then imwrite())
Since R2014b, websave() has been able to download from URL and save to disk.