[PhunkyPhil]

For me, the idea of nondeterminism was around a computation tree who's branches correspond to possible states of computation.

In the context of a deterministic vs nondeterministic finite automata, a DFA has a linear computation path from the root to an accept/reject state and a NFA branches on epsilon transitions, continuing each potential computation (the "guesses") in so called "parallel universes" until one branch hits an accept state.

This definition follows with Introduction to the Theory of Computation 3rd edition by Sipser (would recommend)