The principle of utility states that an action is "right if it produces as much or more of an increase in happiness of all affected by it than any alternative action, and wrong if it does not" [1]. Its basis is the idea that pleasure and happiness are intrinsically valuable, that pain and suffering are intrinsically disvaluable, and that anything else has value only in its causing happiness or preventing suffering. To distinguish it from intrinsic value, this latter kind of value is given the name "instrumental" (or, less commonly, "extrinsic") value, and represents value (usefulness) as means to an end - that end being intrinsic value.
A utilitarian is someone who accepts the principle of utility - and is therefore concerned with maximising the value (utility) of the universe - which makes utilitarianism a consequentialist (goal-based) theory of ethics, as opposed to a deontological (rule-based) theory.
Utilitarianism is concerned with happiness, and utilitarians accept the idea that value is universal - so utilitarians believe that the intrinsic value of happiness it is unaffected by the identity of the being in which it is felt. Thus each counts for one, and none for more than one and my own interests cannot count for more, simply because they are my own, than the interests of others. Utilitarians support equality by the equal consideration of interests - they reject any arbitrary distinctions as to who is worthy of concern and who isn't. This means that we reject egoism, racism, sexism, speciesism, and other forms of unfair discrimination. It does not mean that we deny that there are differences between individuals or between groups of individuals (some individuals are cleverer, taller, stronger, more emotional etc than others), just that there is no logically compelling reason for assuming that a difference in ability justifies any difference in the consideration we give to their interests.
Utilitarians believe that while "happiness", "pleasure", "joy", "satisfaction", "ecstasy" and so-on are not synonyms, they do all represent positively intrinsically valuable feelings; and that the value they represent is of a similar kind, and so is convertible or equivalent (in some proportion). "Pain", "suffering", "unhappiness", "agony" etc are all regarded similarly - that the disvalue they represent is convertible, not only with that of the other negative feelings, but with the positive feelings too. This means, for example, that a utilitarian might believe that it is worthwhile to endure a certain amount of suffering now, if it ensures a greater amount of happiness later.
(Use of the word "pain" is sometimes avoided because of ambiguity: a masochist might be said to be feeling "pain", but they must feel it as "pleasure" - ie. a positive not a negative thing. In ordinary usage, this positive meaning of the word is excluded.)
DMU is a term used to describe the phenomenon where the interests of a well-off individual are furthered to a lesser degree than would be the interests of a less well-off individual by the same thing. For example, a wealthy USAmerican man is generally helped less by the gain of $10 than would be a poor USAmerican man. It is the effect that occurs past the "point of diminishing returns" - where something gets harder to do the more it is done.
In classical utilitarianism, happiness is regarded as positively valuable, and unhappiness (pain, suffering etc) is regarded is negatively valuable. Negative utilitarianism denies the positive aspect - it denies that happiness is intrinsically valuable. By negative utilitarianism, the only goal (the only thing which is seen as "good") is the reduction of suffering. Regular utilitarians and negative utilitarians agree on some issues, and disagree on others. A standard disagreement is illustrated by the fact that a negative utilitarian would believe that, if it were possible to exterminate all life in the universe instantly and painlessly and permanently, it would be correct and ethically required that we do so (in order to prevent any future suffering). A classical utilitarian might decide either way, depending on their estimation of the relative amounts of future suffering and happiness.
Peter Singer has written a very good book on the subject, giving numerous examples of utilitarian consideration. It is called "Practical Ethics" and is highly recommended. He has also written some other good books, of which "Animal Liberation" and "How are we to live?" are particularly useful.
1. The version of utilitarianism described here is, in some ways, "non-standard". The "official" version of the theory is defined in works by Jeremy Bentham, and John Stuart Mill - this version being based on the system described by Peter Singer (see Practical Ethics).