Own widget or whatevery is name for that on myspace or facebook

Let say we are social networking for pets and every user have own profile where he is introducing pets.

What do we need to make if we want that user can just simply copy a code or whatever is name for that to their profile on other social networking site and user from other social networking sites see in that profile an image "My pets" which will lead to profile in our site? Like del.icio.us has.
Is that tagging or what is the name for that?

Thanks

Well, it depends how smart you want that 'My Pets' widget to be. If it's just a link to their profile, then that's all it is. But if the widget needs to display data about their pets, then you'll need remote data parsing, and then present it in HTML, a dynamically generated image, or flash