Mill’s Utilitarianism, chapters 1 and 2 are used to explain the most basic definition of utilitarianism. Chapter 1 presents his opening remarks; his second chapter works toward giving greater detail for the points made in the opening section.
Mill’s intention in writing this book was to explain the Utilitarian or Happiness Theory. It is Mill’s opinion that the Happiness Theory can be used as a test of right and wrong (morality). Mill makes the following arguments in support of this idea. Actions are right in proportion as they tend to promote happiness, wrong as they tend to produce the reverse of happiness.
Of two pleasures, if there be one to which all or almost all who have experience of both give a decided preference, irrespective of any feeling of moral obligation to prefer it, that is the more desirable pleasure.
According to the Greatest Happiness Principle…the ultimate end…is an existence exempt as far as possible pain, and as rich as possible in enjoyments…
…the happiness which forms the utilitarian standard of what is right in conduct is not the agent’s own happiness, but that of all concerned.
…happiness is a good: that each person’s happiness is a good to that person, and the general happiness, therefore, a good to the aggregate of all persons. Happiness has made out its title as one of the ends of conduct, and consequently one of the criteria or morality.
Through these arguments, Mill did a good job of explaining the utilitarian, or happiness, theory and in supporting his opinions against those of his objectors.
It is my understanding that the happiness theory, on its most basic level, says that mankind works to achieve happiness for self and others, and that it is those actions taken to achieve this happiness that are considered moral. It is also important to understand that while the ultimate happiness may not be achievable (as pointed out by those who disagree with the theory), it is the act of working toward this good that finds people behaving morally.

Mill makes the point that “A test of right and wrong must be the means, one would think, of ascertaining what is right or wrong, and not a consequence of having already ascertaining it.” I found this to be an interesting comment.