Refurbs can be the customer changing their mind and shipping a perfectly working product back, or they can have some parts that need to be repaired/replaced. They live up to standards of a new product (with a possible exception being the cosmetics), and they are then sold refurbished.
In the case of the ipods, they look completely new, supposedly. On the other hand, my refurb belkin folding kbrd worked but had some minor scratches on the lid (in normal use, it gets scratchy anyway, so I don't care).