Click the little box beside each pic you want to move to a new album. A green checkmark should appear in the box. Scroll way down to the very bottom of the page. Click "Move Selected". That will take you to another page where you can pick which album to move them too. You can move as many as you want at a time. (Oh, I just realized I have a premium photobucket account, but I assume it works the same on the free ones)

If you have posted the pics you are moving on line somewhere, they will no longer be visible. Moving them breaks the old links.