Up to now I have just loaded specific images from my media folder. But several places refer to image url, such as jetpacks image widget. Does this mean I need to upload the image via ftp outside of wordpress and have a url of e.g. http://mywebsite/stuff/myimage.jpg?
No, if you look in your Media Library from the WordPress Admin panels, and click on an Image you want to use, you will see File URL in the right sidebar. That is what you are looking for.