This passage from the essay Self-Reliance follows Ralph Waldo Emerson's remarks about people's reluctance to change their opinions that have already been approved by others. That is, people are disinclined to adopt new thoughts because they fear that new ideas may disappoint those who have previously approved of their others.
In his essay Emerson emphasizes the importance of thinking for oneself and trusting one's own thoughts:
The other terror that scares us from self-trust is our consistency; a reverence for our past act or word, because the eyes of others have no other data for computing our orbit than our past acts, and we are loath to disappoint them.
Emerson counters that this consistency is foolish because such rigid consistency in thought and action often prevents people from changing, growing, and developing their own potential. To be consistent is, to Emerson, as though the man were "clapped into jail by his consciousness."
Consistency of opinion and complacency in one's ideas and opinions is a terrible compromise of one's individuality, Emerson insists--"With consistency a great soul has simply nothing to do." There can be no growth or development in the person who does not change his thoughts. Further, Emerson encourages individuals to not be afraid to be misunderstood. He mentions that Pythagoras, Socrates, Galileo, and Newton all were misunderstood, along with "every pure and wise spirit that ever took flesh." In fact, Emerson concludes that "To be great is to be misunderstood...." because greatness looks to the future that no one can truly understand until later.
What Emerson means here is that you should not get too caught up in making sure that you have the same ideas one day as you had the day before. That is what he means by consistency -- it is looking like you do not change your mind a lot.
Emerson thinks that it is stupid to be afraid to change your mind. This is what he means when he says that "a foolish consistency is the hobgoblin of little minds." He says that we should change our minds whenever we think that it is the right thing to do. That is part of the idea (a big one for the Transcendentalists) that we should always follow our consciences and do what we think is right at any given time. Here's my favorite quote on that idea:
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.