Sympathy
The foundation of Smith's theory of moral sentiments is the idea that people render judgments on the actions of others by sympathizing -- that is, by using imagination to project how they might feel if they were in different positions. It is even common, according to Smith, for one individual to see both sides of a situation. For example, if you see someone exacting revenge upon someone else for a purported injustice, you will enter into the perspectives of both people in order to determine whether the revenge exacted is justified.
Appearances
Because Smith argues that the basis of moral judgments is sympathy, a consequently essential component of his theory is the degree to which people modulate the appearances of their sentiments in public. We are necessarily more interested in our own affairs than other people are; on account of this, Smith argues that we typically temper the outward expressions of our feelings so that people can more easily sympathize with our feelings. For example, if someone is cheated and becomes infuriated on account of this wrong, the wronged individual should only express a civilly offended demeanor outwardly. Thus, observers can sympathize without seeing one's behavior as self-indulgent or unreasonable. Such a capacity to restrain one's passions, according to Smith, constitutes the virtue of temperance, which is another reason why people appreciate the modulation of appearances: an observer knows first-hand just how difficult it is to exert control over strong passions, and so admires anyone who can do so gracefully.
Conscience
The conscience, our inner moral guide, fits into Smith's framework of sympathy-based morality extremely well. According to Smith, the conscience is, in essence, the third party to our actions; through the operations of conscience, we are able to imagine how our own actions might appear to observers before we even act. Because morality is grounded in the ability of an observer to sympathize with an agent, the imaginative capacity of conscience effectively allows us to test the moral fiber of what we might do. By adhering to the guidance of conscience, we can live lives that are morally-informed and just.
Justice
According to Smith, justice is unique among moral virtues because it alone can be justifiably enforced under threat of punishment. While other virtues are laudable and merit approbation when present, justice is what is owed to ourselves, to each other, and to society in general. Similarly, Smith finds that being just is not praiseworthy in the manner in which benevolence is, for one can be both just and cold towards others; however, a violation of justice is far worse than a deficiency in a different virtue. Again, the reason why this is so, as Smith explains, is that justice is what constitutes the proper treatment of others in terms of abstention from offense. It is worse to commit a positive offense than to not do someone a favor.
Harmony within Systems
Like many of the men and women of his time, Smith was very religious, and this religious spirit comes through in his reliance on the presence of God as a concept in his philosophy. Specifically, Smith utilizes the idea of intelligent design to explain how systems -- such as society -- work so that all of their pieces function in harmony. This theme of coordination comes through, for example, in the famous metaphor of the "invisible hand" which guides the distribution of wealth in society based on the natural state of social classes: because high-class people are not inherently capable of consuming more resources and more pleasures than lower-class people, the surplus of pleasures and resources that is generated through wealth ends up also bettering the lower-class people in the vicinity of high-class individuals (182).
The Difference in Magnitude between Positive and Negative Sentiments
Smith makes a general distinction between sentiments which are positive and those which are negative. He argues that the average person has far less to gain than he or she has to lose. Therefore, people are very unlikely to take risks unless they have substantial incentives to do so: for example, the acquisition of glory through exploits of significant heroism could be exactly such a strong incentive. It is for the same reason that people are more inclined to respect those who maintain their dignity and sense of grace when they have suffered significant losses than those who have decided to sacrifice positive opportunities: it is much more difficult to handle the loss of what one already has gained than the loss of what one might have hypothetically gained.
The Corruption of Moral Sentiments by Wealth
Though Smith believes that respect for and admiration of those who are wealthy are necessary for maintaining the proper balance of classes in a given society, he also sees this respect and admiration as primary causes of moral corruption. People become accustomed to seeing the great respect and admiration given to those of wealth and status, and therefore admire the wealthy more than the wise (who are often not in the public eye). The net result of this tendency is that the population at large ends up misconstruing wealth as virtue; rulers are consequently able to commit morally-questionable actions with the approval of their people.