Utilitarianism is a philosophy based on pleasure seeking; its basic principle is "the greatest happiness of the greatest number". So a utilitarianist would aim to produce most happiness for most people, but if that is not possible, he should aim to reduce the unhappiness of the greatest number. This kind of thinking reduces self-interest pursuit (egoism) and encourages helping society. Since this philosophy is concerned about producing happiness it's a consequentialist theory, because consequences do matter and they determine a lot, because they show if an action is morally right or wrong. Utilitarianism was founded by Jeremy Bentham in 18-19th century.
Utilitarianism, like any other philosophy, it has its flaws and strengths. Utilitarianism lowers human integrity, which gives more responsibility to us. We can use this story as an example, there are 10 Indians, either they are all shot or you can shoot one and others will be saved. By utilitarianism principles it is better to take the second choice because that is the action which will cause minimum unhappiness, but then if you do shoot the one Indian we can say that you were directly responsible for his death, which gives you more responsibility. Either you shoot one and the rest are happy that they survived but you are directly responsible for a person's death or you can do nothing and everyone will be shot but you won't be responsible for anything. J.Bentham would argue that it's still better to shoot only one because that would be the least unhappiness caused, one person's death is better than 10 deaths. Another major problem with utilitarianism is that it's a consequentialist theory and there are no rights regarded to actions. To calculate a consequence the hedonic calculus is used which uses 7 key factors to determine which action would have the best consequence: Duration, Intensity, Propinquity, extent, certainty, purity, fecundity.