Reference a broad type of relationship that goes from words to things - somehow the words and phrases link to the world. When one uses a word or linguistic expression, those expressions serve as pointers of some kind to things in the world. Philosophers working in the philosophy of language have tried to understand how this relationship work in a variety of different cases: names, general terms, indexicals and definite descriptions being some. There are some difficult issues that reference brings up: whether or not one can refer to something which one does not have knowledge, questions surrounding the radical translation project of Willard Van Orman Quine and the status of negative existential statements.
A wide variety of things have proper names. 'Barack Obama', 'London', 'the Atlantic Ocean', 'Ganesh', 'Saturn' and 'Oxfam' are all proper names. Proper names get assigned to people, places, organisations and even supernatural or fictional entities: 'Harry Potter' and 'Gandalf' are used as proper names. How do you get from the use of these terms to the things which they represent?
There are two main theories in philosophy for how this is done: through the use of a definite description or through a causal account. Some philosophers have merged this two accounts.
Descriptivist accounts of proper names
Gottlob Frege and Bertrand Russell are usually given as examples of the two best-known defenders of the descriptivist account of names. According to this account, when one uses a name like 'London' or 'Barack Obama', the words are a kind of shorthand for some description that uniquely picks out the referent. So, if one has a statement like 'Barack Obama is visiting Montana', what one is actually saying is '(the current United States president) is visiting (the 44th most populated state in the Union)', or something equivalent.
Descriptivist accounts are useful because of the theory of meaning that they bring with them: it is clear how one figures out whether or not 'Barack Obama is visiting Montana' is true on a descriptivist account: you simply use the descriptivist's set of truth conditions to analyse.
But there are problems: as Frege pointed out, names have senses as well as (descriptive) referents. A sentence such as 'The Queen is not really the Queen' ends up not having the meaning most people would have when they say it. For most people, such a sentence would mean that the Queen of some particular country, say Queen Elizabeth II of the United Kingdom, is not rightfully the Queen. Perhaps there is some bizarre situation where the Queen died and someone else is pretending to be her until her successor is popular enough to take their place at the throne.
Secondly, a descriptivist theory is epistemically dependent: for a name to have reference, one must know enough about the referent to uniquely identify them. Most educated people in the Western world may know enough about some prominent political leader like Adolf Hitler or Winston Churchill to be able to uniquely identify them, but if all one knows about Hitler is that he is "a dictator and great orator", one does not uniquely identify him in comparison to other dictators. Yet one can still use the words 'Adolf Hitler' in a satisfactory manner in a sentence, like "I have heard Adolf Hitler was a great orator, but a brutal dictator", even though neither your sentence, nor the knowledge which gave rise to your sentence have enough content to definitely describe the person.
Thirdly, it seems utterly strange to say that two people can refer to the same person based on two different definite descriptions: if Alice says something about Thomas Paine and has in her mind only that Paine was the author of The Age of Reason, and Bob says something about Paine and has in his mind that Paine was the designer of the Sunderland Bridge, what actually makes it so that Alice and Bob are both talking about the same person? To alleviate this, some have suggested the so-called "cluster theory". Under this theory, each proper referent has a cluster of definite descriptions which pick them out uniquely, and correct reference is made by use of any of the members of the cluster.
The causal theory of names
Ruth Barcan Marcus and Saul Kripke have criticised this view of names and provided an alternative: the causal theory of names. The causal theory manages to avoid most of the problems of the descriptivist theory, and it is widely accepted that some form of the causal theory is probably right among analytic philosophers.
The causal theory is very simple: what makes a name have reference is that there is a causal chain of name usage going back to some baptism event (which can, when appropriate, be a formal or religious ceremony of naming but usually is just simply someone pointing at some object and saying the name). The causal chain need not be oral - when a contemporary philosopher says 'Plato', the causal chain may have passed through their professor, or it may have gone through some book they read as a student that mentioned Plato. Either way is fine, so long as, if one were to check (and it were possible to do so), the chain would eventually end back during Plato's lifetime or whenever Plato was named Plato. Kripke notes that sometimes things may be named in a contingent, a priori manner, perhaps through use of a conditional ("if we have a girl, we're going to call her Kate") or a counterfactual ("if you had been a boy, you would have been called Daniel"). Sometimes a reference is fixed using a definite description: Kripke gives the example of Urbain Le Verrier's naming of the planet Neptune, where he made a mathematical prediction (which serves as a definite description) and then the planet happened to fit the definite description and was thus named. We do not now refer to Neptune by reference to the definite description which Le Verrier used during the discovery - that only fixed the reference of the name, which we now get through reading science books or being taught the names of the planets in school.
In the Hitler example, one would refer to Hitler even though one does not have enough knowledge to uniquely refer to Hitler, so long as there is a causal chain that goes back to the initial baptism of Hitler.
There is a problem with the causal theory, and that is the problem of reference change. This problem was raised by Gareth Evans, who points to a number of examples: that of Marco Polo's naming of Madagascar and the fictional case of two babies being switched in a hospital maternity ward and growing up with each other's names. Michael Devitt has modified the causal theory to account for reference change - under this account, reference is set further by each use of the name.