Deborah nailed it, just one small clarification:
As a result, attachments are not copied when you quote a post, but images are. That way the picture is not copied in every post, and the forum takes up less space on the server.
Other way around--attachments take up space on the server, so with attachments, the first part of the sentence is correct, it's not copied on every post, but the second part isn't (embedded images take up zero space, or rather, just the space that the plaintext link takes, which is a few kb, whereas attachments take up whatever space the size of that file is--e.g. if I upload a picture to the forums, it may take 2-3MB, but if I link to a picture, it may take 2-3KB (1000x less) to save that text on the forum for the link to the picture).
Unless I misunderstood that second part, where you were talking about what takes up less space, but I think you were saying that about attachments (by starting the sentence with "That way the picture is not copied in every post," which is the case with attachments). But if I did misunderstand, and we're on the same page, no worries, hopefully that clarification helped anyone else who read it how I did. :)
Are you familiar with attachments in emails, Diane? That may help you think of the distinction. To simplify, an attachment is uploaded to that particular email (or post, in this case). When you reply to the email, even quoting the text, the attachment isn't there, it's still just "stuck" onto that original message. An embedded picture is hosted elsewhere on the internet, and displays within the post (or email). It's essentially a code telling your computer "go get this image from this website, and display it here in this post" so when you quote it, you're quoting that code, too, so your quote does have the image as well.
Did that make sense?