Help:Editing

Brilliant but just one question..How when i open my cut out image into a new bacourkgnd, how do i keep it as just the bit i cut out when i go the image? (as soon as i go it, i am moveing the cut out part so that i get the bacourkgnd instead of the image so in my case, i get a horse shape, but just the bacourkgnd/some parts of the horse from the original photo) it's kind of hard to clarify..