The short answer is:
Actions are right to the degree that they tend to promote the greatest good for the greatest number.
"an action is right in-so-far as it tends to produce pleasure and the absence of pain" John Stuart Mill
Utilitarianism seems simple enough on the surface. The idea that the right action is the action which will promote the greatest good for the greatest number of people.
Let's use organ transplantation for example. If someone goes on a routine medical check-up and is found to be in perfect health, living a normal life etc... and is not likely to discover the next new cure for cancer or energy source, his doctor could do the greatest good by killing him and harvesting his organs. This is Act Utilitarianism. This would not encourage persons to visit the doctor for a routine check up.
So doctors have a rule: First do no harm. The patient trusts that the doctor is not likely to kill him or her for the kidney, liver, or other organs that may be useful to some other persons. The individual with the healthy organs continues to live and be happy and healthy. And the Doctors practice a form of rule utilitarianism. If this otherwise healthy person is severely injured in a car crash, his or her family may be encouraged at the bedside to donate the organs.
The utilitarian view of the person is that the person's happiness is sought after by the most useful means to society. Utilitarianism has been called "the doctrine of swine" because its highest endeavor is the pursuit of pleasure.
As far as society, the greatest good for the greatest number of persons may be harmful to some persons. If everyone follows the rules, most of society is happy and free from pain.
A utilitarian view tells that the value or worth of a deed that one does is determined by its contribution to society. The reason it is called a utilitarian view is because this contribution to society is sometimes called an action's 'utility.' In layman's terms, utilitarians believe that the ends justify the means. In other words, how valuable the action actually is can be defined by how much and how positively it affects society, or its outcome.