I am studying finite state automata and learning how to prove a machine uses the minimum number of states. I have come across the Myhill-Nerode theorem and one of the corollaries states the following
Corollary. For a deterministic finite automaton M, the minimum number of states in any equivalent deterministic finite automaton is the same as the number of equivalence classes of M's states.
My question is, what does "equivalence classes of M's states" mean?
Thank you for your time!