You don't just put the URL in your post, you have to tell the system it's a photo (image)
To do this automatically, when you make your post (or your signature, wherever you want the photo to appear), put your cursor where you want it, paste the URL, then highlight it and click the image icon which will put the image tags around it.
Or even easier, just type the image tags yourself. When you're done it will look something like this:
[ img]http://www.photobucket.com/imagecodes/photoidentifier/photoname.jpg[ /img]
Note: Do NOT enter the spaces I put in the image tags. Spaces are there in this example only so the system doesn't think it's a real image somewhere