Hume begins by pointing out a mistaken belief that folks often hold: the idea that morality is based entirely on reason. Arguing that sentiment also plays a major role in our moral judgments, Hume spends the earlier part of the Enquiry discussing the social virtues—i.e., benevolence and justice. These two virtues work in different ways, but Hume emphasizes that usefulness (to both ourselves and others) is a major factor in our moral thinking.
Following his emphasis on usefulness, Hume examines why this quality is so valued. He then zooms in on some characteristics that are seen as useful, recognizing that this can vary depending on culture/time period. These characteristics can be mental, emotional, or physical, and Hume includes plenty of examples. However, Hume recognizes that some qualities—such as politeness, wit, and decency—are immediately agreeable; regardless of utility. Hume then criticizes "monkish virtues" (XI.I.3) like solitude and fasting, as these aren't agreeable or useful. He concludes with a moral message of his own: some people may give in to greed and temptation, but what they fail to realize is that it's the natural pleasures that are priceless.
In the four appendices that round out the Enquiry, Hume summarizes his key arguments. He begins by recapping his main point, which is that it's not reason alone that shapes our sense of morality, but sentiment too. He then argues against the idea that we're entirely driven by selfishness, and goes on to sum up what makes justice different from other virtues (namely, that it's not immediate and instinctual like benevolence is). Hume ends by stressing that we shouldn't get preoccupied with wording—if we refer to "a vice" or "a crime" we're dealing with a similar type of thing.