In this book, David Lewis sets out to provide a working definition of convention and then attempts to demonstrate that language is conventional in the more precise sense in which he uses the word. A convention, according to Lewis, is a regularity in the behavior of members of a group across similar situations, when and only when it is both true and known by the members of the group that across the similar situations 1) almost everyone will conform to the regularity, 2) members of the group will have mostly the same preferences regarding the possible actions, and 3) the members of the prefer would prefer themselves and the other members to conform to the regularity as to some other regularity (adapted from 78). Lewis demonstrates that a person could construct a simple language that operates according to this definition, and so be conventional in his sense. He also tries to show that a complex language could be conventional. However, even if his reasoning that a complex language could be conventional is sound (I'm not sure if it is; it was a difficult argument for me to understand), it does not follow that language in the real world is conventional, which is what Lewis would like to prove. Take the second necessary condition above, that members of the group have mostly the same preferences regarding possible actions. For language to be conventional, then, speakers of a language (that is, members of the said group) would have mostly the same preferences regarding language use (possible actions). As a matter of fact, however, speakers have an infinite variety of ways to generate sentences and an infinite variety of ways to initiate and respond in conversation, to take a couple of examples. If this is the case, then no speaker of a language could have most of the same preferences for how to use the language. Therefore, language is not conventional. A more complicated story of language is told in linguistics, namely in its conception of an ur-language as a natural endowment of human beings, which itself is capable of producing the complex variety of spoken, written, and signed languages on the basis of adjustments in cognitive 'parameters' regarding syntactic structures, the adjustments being the result of environmental 'triggers' vis-a-vis human beings. This hypothesis is the predominant view these days, and which seems to have the most support.
Even though Lewis might be wrong about language, it does not deter from the usefulness of his working definition of a convention and its application to other aspects of human behavior, especially in its potential explanatory power for how humans socially organize. Matters ranging from driving on the right side of the road in the United States to the Milgram experiment could fall under the category of human adherence to convention. Thus, just because Lewis did not adequately explain language does not mean that the concept he attempted to use to explain language should be dismissed.
Also, Lewis provides a working definition in his book of a social contract to contrast it with convention. A social contract, according to Lewis, is a regularity in the behavior of members of a group across similar situations when and only when it is both true and known that 1) members of the group in some relevant situation will conform to the regularity, and 2) the members of the group prefer to conform to the regularity than not to conform to the regularity, where not conforming to the regularity would lead no members of a group to anticipate a regularity across situations (paraphrased from 88-89). If this definition seems too close to a convention, Lewis further clarifies in the following way. "For convention, we require that each agent prefer general conformity to conformity by all but himself [sic:], ignoring his preferences regarding states of general nonconformity. For social contract, we require that each agent prefer general conformity to a certain state of general nonconformity, ignoring his preferences regarding conformity by all but himself [sic:]" (90). That is, for a convention, a person would just prefer that she and the others conform to this regularity and not to some others, whereas in a social contract, the alternative is no regularity at all, and so of utmost importance to the person is that everyone conforms to the regularity, without which there would be no regularity to conform to at all. For example, Hobbes argues that without conforming to the rule of law (the regularity), human beings resign themselves to a life that is nasty, brutish, and short (no regularity at all).
Overall, it was a good read. You should read it if you like philosophy. If not, you probably wouldn't like it.