The example shows links to pictures, but not embedded pictures themselves. vBulletin supports allowing pictures to be directly embedded into the thread - you see them on the page with the message, but the admins have disabled that feature. Pictures can make moderation more difficult. So long as pictures are required to be hosted elsewhere, no bandwidth problems arise but there is typically extra support required to answer questions about why all the picture links are broken whenever the off-site photos are deleted and to investigate cross-linking of copyrighted materials or inappropriate content within the pictures. I suppose that is the reason they are disabled, but they do add a lot to a site and it would be nice to see them enabled. For now links to off-site pictures is the best we have, or at least the best I am aware of, not because that is all that is technically possible but rather because that is all the admins have decided to allow.

EDIT (to answer OP's question): You include the link by clicking on the picture of the globe with the chain links in front of it. It then asks you for the test to be displayed and the actual link. Just be sure the address you enter goes directly to a photo hosted on a website. GL!