What does, "A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines" mean?

This statement comes from the Transcendentalist tradition, of which Emerson was a major thinker.  Transcendentalists believed, among other things, that it was important for each person to follow whatever their conscience told them at any particular time.

The line you quote expresses this idea.  It says that only "little minds" need to feel like they are being consistent all the time.  A greater mind would not be bothered if the idea it has today contradicts one it had yesterday, as long as it (the mind) follows what it sincerely feels at any given time.

So -- the quote is saying that only little minds (like those mentioned) would worry about seeming consistent.  Greater minds just follow whatever they think at any given time.