This is a great question. Structuralism started with the linguistic work of Ferdinand de Saussure and the Prague and Moscow schools of linguistics. The basic thought of this approach to linguistics was not to study the use of language, but the underlying structure of a language (hence, the name structuralism). More specifically, this approach sought to study how elements in language relate to each other. Saussure, therefore, spoke often about the signifier and signified in language.
In the end, there were many critics of this approach to language (such as Noam Chomsky), but not before many other scholars took the ideas of Saussure and applied it to other fields of study. Eventually structuralism played a large role in various fields such as sociology, anthropology, and literary criticism. The chief insight was that there was a system or structure in place. If a person could map out that structure, then meaning could be located. Today there are many critics, but the basic insight of structuralism is still a useful theory to look at data in a fresh new way.