Solipsism, when held by person X, is roughly the idea that person X is all that exists, and that everything external to X is merely a fabrication. This is what I will refer to as the metaphysical conception of solipsism. True solipsists in this sense are few and far between. Perhaps this is due to the fact that whenever any two solipsists meet, at least one of them is necessarily incorrect. Hence, the humor in the notion of a “solipsist convention.”
A more viable and widespread, although still unpopular, conception of solipsism is what I will call the epistemological conception of solipsism. Proponents of this view do not necessarily believe that they are the only existing things, but only that we cannot know of the exitence of anything external to oneself. Consider an argument made famous by René Descartes: “I think, therefore I am.” This valid inference gives me motivation to think that I, in fact, exist, for even if I were being massively deceived by an evil demon with respect to every one of my experiences, it could not be that the demon is able to deceive me with respect to my belief in my own existence. However, since I do not have this sort of first-person perspectives into the minds of, for example, you, it is possible that I exist and nothing else.
For more on solipsism and The Problem of Other Minds, see the article in the Stanford Encyclopedia of Philosophy.