This might best be explained by example. Suppose Zachary believes in the general principle of always obeying the commands in the Bible. Suppose also that he thinks that it is not ethical to stone people to death merely for being Wiccan. These views may come into conflict (see Exodus 22:18). If they do, Zachary will then have several choices. He can discard his general principle in search of a better one (for example, only obeying the Ten Commandments), modify his general principle (for example, choosing a different translation of the Bible, or deciding to interpret the commands figuratively), or change his opinions about the point in question to conform with his theory (by deciding that witches really should be killed). Whatever the decision, he has moved toward reflective equilibrium.
Reflective equilibrium is not static; it will change as the individual considers his opinions about individual issues or explores the consequences of his principles.
Rawls applied this technique to his conception of a hypothetical original position from which people would agree to a social contract. He arrived at the conclusion that the optimal theory of justice is the one to which people would agree from behind a veil of ignorance, not knowing their social positions. See the article on John Rawls for more information about his theory.