A hobgoblin is a small, mischief-making imp from folklore and fairytales whose intentions are usually evil.
In this statement, Emerson uses hobgoblin as a metaphor, comparing the abstract term "consistency" to the concrete image of a hobgoblin. This works well for Emerson's purposes, as he wants to belittle and warn his readers away from consistency. Hobgoblins would bring up in people's mind the idea of a minor evil or nuisance. Relating these evil but somewhat silly creatures to consistency diminishes and devalues the idea of consistency, changing it from a virtue to a vice.
This underscores Emerson's main point in the essay: an individual should follow the prompting and "vibration" of their own soul and not be held back by tradition, their parents, or the past. Consistency—doing what you or your family always did before—becomes a problem and a distraction: an evil that Emerson wants his listeners to shake off. Until the individual discards the idea that he has to be consistent, this concept will haunt him and make mischief in his life.
Emerson wants his readers to trust themselves. Out of this self-reliance, he argues, have come the great men who changed the world. America can become a great country if people shake off superstitions and old ideas that keep their minds "little" or unimaginative.
In his essay "Self-Reliance," Ralph Waldo Emerson emphasizes the importance of trusting yourself and following your own ideas and instincts. Envy, he tells the reader, is ignorance, while "imitation is suicide." There is no point in your existence if you merely copy somebody else.
This message, while Emerson expounds it with great eloquence, can be gathered from the title of the essay. However, it is not enough simply to rely on yourself. You must be able to review and revise your ideas. As Emerson puts it,
Speak what you think now in hard words, and tomorrow speak what tomorrow thinks in hard words again, though it contradict everything you said today.
You must not only avoid conformity with others, but also with your former self. This is what Emerson means when he says that a "foolish consistency is the hobgoblin of little minds," which is so popular among various authority figures. When you think about a matter, you should not copy what Moses, Plato, or Milton thought. They did not imitate anyone else, which means that by copying them, you are, ironically, acting in a manner unlike them.
However, you should also avoid copying your former self. You should treat what you thought yesterday as an authority in the same way that you treat Plato as an authority and not be afraid to deviate from it if you think you have a better idea today. It is only small-minded people who refuse to change their minds in the name of consistency.
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.