Nuclear fission works by a neutron (a tiny particle) hitting an atom of uranium-235, causing it to split into two new atoms, both of which are smaller.

These new atoms can't be used in a nuclear reaction but still have a lot of mass (only a teeny amount is turned into energy) so the spent fuel rod still has a mass which is almost identical to the "new" rod, hence a lot of waste being produced after the reaction because these new atoms are quite unstable in their own right.