CDDR function is composition of two CDR functions. That is, (CDDR X) is same as (CDR (CDR X)). There are other CAR and CDR combinations, see HyperSpec, CAR and CDR.

(cddr '(1 2 3 4)) => (3 4)
(cddr '(1 2 . x)) => X
(cddr '(1 . nil)) => NIL
(cddr nil) => NIL