What does, "A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines" mean?
I agree with the above response, but I would emphasize that Emerson is not just talking about being consistent with other people's ideas. He is also talking about not worrying about being consistent with our own previous ideas. That aspect of what he is saying is illustrated by the following passage that comes two sentences after the line you quote:
Else if you would be a man speak what you think today in words as hard as cannon balls, and tomorrow speak what tomorrow thinks in hard words again, though it contradict every thing you said today.
The essay "Self-Reliance" is mostly about nonconformity and individualism, showing that to be truly self-reliant one must not only do for oneself but also think for oneself. The idea it to "trust thyself." The quote above basically means that blindly following someone else's ideas is foolish and small-minded, only appreciated by the people being followed, and leaving nothing for the follower. Hobgoblins refer to fanciful creatures, small and childish, delighting themselves in pranks and jokes (Shakespeare's Puck from A Midsummer Night's Dream, for example). Consistency results in nothing but folly for the follower and adoration for the followed. Emerson promotes the idea that "to be great is to be misunderstood," reiterating this philosophy that true self-reliance means being completely original and spontaneous, following one's heart and not pre-established ideas and principles.
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.