You need to send an HTML email (not plain text).
Find examples using Google: http://www.google.com/search?q=php+h...il&btnG=Search
You have the right idea though about the image being a remote link. Even with HTML emails, images are referenced from remote sites. If someone doesn't allow HTML emails, or have some sort of "safe mode", they will just get a box with an -X- where the images should be.