Working on P.D. Magnus. forallX: an Introduction to Formal Logic (pp. 267, exercise A. 1), asks:
Show that each of the following is neither a validity nor a contradiction:
$D(a) \wedge D(b)$
Do I need to bind $a$ and $b$ to elements of a domain ?
What's an interpretation in this context?
One usually only speaks of "binding" in the case of variables getting bound by quantifiers. $a$ and $b$ are names. As specified on p. 248, an interpretation assigns to each name an object from the domain.
So what you have to do is finding one pair of a domain and an assignment of $a$ and $b$ to objects from that domain such that $D(a) \land D(b)$ gets false (to refute validity), and one domain + interpretation such that it gets true (to refute contradictoriness).