Superficially, honesty means simply stating facts and views as best one truly believes them to be. It includes both honesty to others, and to oneself (see: self-deception) and about one's own motives and inner reality. Honesty, at times, has the ability to cause misfortune to the person who displays it. Honesty can also mean fairness, and truthfulness, and the avoidance of misleading people.
The concept of honesty applies to all behaviors. One cannot refuse to consider factual information, for example, and still claim that one's knowledge, belief, or position is an attempt to be truthful or is held in "good faith." Such willful blindness is clearly a product of one's desires and simply has nothing to do with the human ability to know. Basing one's positions on what one wants — rather than unbiased evidence gathering — is dishonest even when good intentions can be cited — after all even villains could cite good intentions and intended glory for a select group of people. Clearly then, an unbiased approach to the truth is a requirement of honesty.
Because intentions are closely related to fairness, and certainly affect the degree of honesty/dishonesty, there is a widespread confusion about honesty. There is also a general belief that one is necessarily aware that dishonest behavior is dishonest. But it's at the moment when one willfully disregards information in order to benefit (such as to justify their actions or beliefs) that one shows whether they are interested in the truth or whether they have a lack of respect for the truth, which is dishonesty, regardless of whether they mislabel it stubbornness or conviction. Socrates had much to say about truth, honesty and morality, and explained that if people really understood that their behavior was wrong — then they simply would not choose it. Furthermore, the more dishonest someone is, the less likely they are to understand honesty and to characterize their behavior as wrong. Unfortunately,the meaning of honesty has been marginalized to specific lists of behaviors that more often than not --change over time like fashion. The understanding that honesty requires an unbiased approach to the truth and to evidence gathering at all times (a timeless approach) collides with ideologies of all types. This would explain why honesty, although often discussed -- has failed to become a cultural norm. Ideologies and idealism inherently exaggerate and suppress evidence in order to support their perspectives. They essentially state that their way is the only right way to view the world. This erodes the practice and understanding of honesty and creates ongoing conflicts in all human relationships.
His shallowest concept of honesty was implied in his notion of Li: all actions committed by a person to build the ideal society - aiming at meeting their surface desires of a person either immediately (bad) or longer term (good). To admit that one sought immediate gratification could however make a bad act better, and to hide one's long term goals could cloud a good act. A key principle was that a "gentleman" must strive to convey his feelings honestly on his face, so that these could help each other coordinate for long term gain for all. So there was a visible relation between time horizon, etiquette and one's image of oneself even in the mirror. This generates self-honesty and keeps such activities as business calm, unsurprising, and aboveboard. In this conception, one is honest because it suits one's own self-interest only.
Deeper than Li was Yi or righteousness. Rather than pursuing one's own interests one should do what is right and moral - based on reciprocity. Here too time is central, but as a time span: since one's parents spent one's first three years raising one, one spent three mourning them after they die. At this level one is honest about one's obligations and duty. Even with no one else to keep one honest or to relate to directly, a deeply honest person would relate to ancestors as if they were alive and would not act in ways that would make them ashamed. This was part of the moral code that included ancestor worship, but Confucius had made it rigorous.
The deepest level of honesty was Ren, out of which flowed Yi and thus Li. Confucius' morality was based upon empathy and understanding others, which required understanding one's own moral core first, rather than on divinely ordained rules, which could simply be obeyed. The Confucian version of the Golden Rule was to treat one's inferiors as one would want one's superiors to treat one. Virtue under Confucius is based upon harmony with others and a recognition of the honest reality that eventually (say in old age) one will come under the power of others (say one's children). So this level of honesty is to actually put oneself in context of one's whole life and future generations - and choose to do or say nothing that would not reflect one's family's honor and reputation for honesty and acceptance of truth, such as eventual death.