There are many kinds of conventions, and many kinds of reasons to adopt (or reject) them, but what makes some sort of agreement between people a convention is that they know or suppose it might have been made differently, and that there was no logical necessity to arrive at the convention that was reached.

An excellent example of the importance of conventions are the symbols and terms of natural languages, and another fine example are the notations used in mathematics, but in fact conventions and agreements of many kinds permeat all human societies and interactions.

It has been argued in philosophy that most, or indeed all, of philosophy (metaphysics, science, mathematics, law ....) is in fact conventional, and indeed wholly so, and that the only reason to adopt such conventions as one does is convenience.

But this is not so, except perhaps in a few fields, like the choice of a mathematical notation, or the design of the national flag, since in fact such conventions as are agreed upon tend to have a lot to do with the context in which it happens, and the ends, practices or actions the conventions are intended to facilitate.

Examples of extreme conventionalists, in some philosophical sense, are the early pragmatists Schiller and James, who claimed that all or much of philosophy consists of conventions, and that what was surrected this way was a philosophy of as if, that was quite sufficient for most human ends; early neo-positivists like Carnap, who claimed that the existence of the real world is a linguistic convention, in the end; and radical epistemologists - usually with some hidden political or personal agenda - like Foucault, who argued that all of truth and all of reality is merely conventional.

In philosophy of science, the best arguments for a partial conventionalism are by Poincaré and Duhem, who both showed that parts of physics are more conventional than most people, including physicists, believe. (Thus, for all that is known, it may be that many of the invariances that are assumed by physics, are either purely conventional, or else slowly but unperceptibly changing in sofar as they depend on facts.)

It is generally unwise to insist on radical conventionalism of some kind, unless one is quite good at physics and mathematics, and even then the general plausibility of conventionalism often has more to do with human ignorance or convenience than with total indifference of what the real facts are.

But it is true that there are in every science quite a few parts that are wholly or mostly a matter of convention, such as what is the best terminology, scale of measurement, or notation adopted.

And here it is well to remark that even if something is 'purely conventional', such as e.g. the special symbols used in mathematics or mathematical logic, the choice is usually not purely arbitrary at all, in the sense that 'anything would do, anything goes', but much constrained by desires like easy readability and easy writability, and some sort of intuitive appeal. There have been various notations in logic, such as Frege's or (reverse) Polish notation, that are quite (in)famous for unreadability. (This paragraph also applies to programming languages. It so happens that reverse Polish notation is as convenient for compilers - mechanical interpreters of formulas and expressions - as it is difficult for humans, approximately.)