Hey Sabrina,

As far as I'm aware, there are two settings on Photobucket. One is private, meaning a URL to your album given to someone without your password wouldn't allow them to get in to see your pictures. They also don't show up on random image searches.

The other setting is public. Pictures can potentially show up on image searches, and anyone with the URL to your album can see the pictures.

(My album is public because I'm not worried about anyone stealing my icons. lol)