A good example of this is the naming conventions for variables..  While in principle any symbol can be used for one type of variable, in practice individual symbols have pre-existing connotations that make it more natural to assign them to specific variable types.  For instance, one usually denotes $x$ to denote a real number, $z$ to denote a complex number, and $n$ to denote a natural number; a mathematical argument involving a complex number $x$, a natural number $z$, and a real number $n$ would read very strangely.  The most famous example of this is perhaps the use of the symbol $\varepsilon$ in analysis; an analysis argument involving a quantity $\varepsilon$ which was very large or negative would cause a lot of unnecessary cognitive dissonance.  In contrast, by sticking to the conventional roles that each symbol plays, the notational structure of an argument is reinforced and made easier to remember; a reader who has temporarily forgotten the definition of, say, $z$, in an argument can at least guess that it should be a complex number, which can assist in recalling what the actual definition is.
As another example from analysis, when stating an inequality such as $X < Y$ or $X > Y$, it is customary that the left-hand side represents an “unknown” that one wishes to control, and the right-hand side represents a more “known” quantity that one is better able to control; thus for instance $x<5$ is preferable to $5>x$, despite the logical equivalence of the two statements.  This is why analysts make a significant distinction between “upper bounds” and “lower bounds”; the two are not symmetric, because in both cases one is bounding an unknown quantity by a known quantity.  (Another relevant convention in analysis here is that it is preferable to bound non-negative quantities rather than non-positive ones, thus for instance $|x| < 5$ is preferable to $-|x| > -5$.)
Continuing the above example, if the known bound $Y$ is itself the sum of several terms, e.g. $Y = Y_1+Y_2+Y_3$, then it is customary to put the “main” term first and the “error” terms later; thus for instance $x < 1+\varepsilon$ is preferable to $x < \varepsilon+1$.  By adhering to this standard convention, one conveys useful information as to which terms are considered main terms and which ones considered error terms.