What is the formal language described by inverting accepting states of NFA? By inverting, I mean that rejecting states become accepting states and accepting states become rejecting states.
Is there a nice expression for such a language reference to the original NFA language?
No. Consider an NFA with two states, $q_0$ and $q_1$, and both $0$ and $1$ transitions from $q_0$ to itself, from $q_1$ to itself, from $q_0$ to $q_1$, and from $q_1$ to $q_0$. Make $q_0$ the initial state, and make $q_1$ the only accepting state. The resulting automaton accepts $\{0,1\}^*$. So does the NFA that you get when you change acceptor states to non-acceptor and vice versa.
On the other hand, if you start with an NFA that happens to be deterministic, switching acceptor and non-acceptor states will give you an automaton that accepts the complementary language. If you play around a bit, you can produce other examples in which you get neither the original language nor its complement.