Conventions in language is an unconcious or at least covert agreement between the speakers of a language of the links between words and morphemes and their meaningful contents. The links are mostly random (altough for instance onomatopeic words have a clear sound link to its meaning e.g. splash). This conventional connection between content and expression is called a sign. Linguistc signs can be combined into a system we call syntax.
However a communicative convention contains not only links between units in the linguistic system, it also contains links to the language users and to the communicative situation. The communicative convention is something we (all human language beings) master better or worse. But for interpreters it is vital, both that we master it but also that we can recognize it and explore it. Think about how, in principle, a language has means to create a common understanding among the speakers of that language. Yet, one language contains so many different registers, dialects, ideolects and sociolects so you can ask yourself whether there is a real possibility to create a common understanding between all speakers of the language. On a very general basis perhaps but when we move past general statements.
Interpreters master not only one language but it is their job to convey meaning from one language to the other (obviously…). In order to convey that meaning they need to be familiar with the communicative convention of both languages, but also of a multitude of different communicative conventions within the two languages. Nowing the convention is to know where it is valid, in which groups it is actively used and where it is perhaps not known at all.