Image Upload Problems

I’ve been trying to upload images to our Sponsor page by using Edit -> Image -> Choose File -> Upload it to the Server. Every time I hit the final button, I receive an error saying that “It was not possible to complete the request due to file system permission restrictions.” I am an admin on the site, so I can’t understand why I haven’t been able to upload images. This problem has persisted over the last few month and is now posing a problem because we have sponsors who are concerned about their broken image links or entire lack of images. 

How can this be fixed?