Language is symbolic in the sense that it consists of a system of arbitrary or conventional signs.
Imagine, for example, that I speak of a "cat." The term cat is a "sign." The sign "cat" can be separated into two components, the noise I make saying the word (or letters on a page), which is a "signifier," and the "signified," or the concept with which the signifier is associated, namely a small furry domestic animal that likes to attack my mouse when I am trying to work.
We understand language as a symbolic system. No one sign is meaningful by itself, but instead each sign accumulates meaning in terms of its similarities and differences to other signs. For example, we might understand "tabby," "Siamese," and "Maine coon" as types of "cat," while "lynx," "bobcat," and "dog" are not domestic cats and thus by thinking about them we clarify the demarcations of our concept of "cat." These demarcations are arbitrary (one could imagine a language that did not distinguish among domestic cat, bobcat, and lynx, for example, or that assigned different signifiers to long- and short-haired cats).
Each language has different conceptual demarcations. Thus when we look at how kinship terms, for example, differ from one language to another, we learn something about how cultures differ.