Well, structuralist theories are concerned with (you guessed it!) structures. But not just any structures -- these are the underlying structures that are beneath the surface of basically everything in human culture. You can have structuralist theories of literature, but also language, psychology, anthropology... and so on and so forth.
The assumption is that beneath the surface phenomena of basically everything under the sun of human organization is an objective structure (determined socially and psychologically) which are assumed to have their own internal logic and can be studied. The structures reveal the important interrelationships between these surface phenomena, as well as the relationships between the phenomena and the underlying structure. Also, you can't know what something means based on its own intrinsic value, but only by how it relates to other things that it's not. [This is the important part, so keep that in mind as we go on! It will make more sense as we explore this field further, I promise.] You could say that structuralist theories attempted to turn fields often considered rather subjective (like literary studies, for example) into something more objective and scientific through this attention to underlying structures.
Many theorists will argue that the field of structuralism was born with the work of the influential Swiss linguist Ferdinand de Saussure, who single-handedly invented structural linguistics and semiotics without ever having to write any influential texts on his own. No, seriously -- his work was only circulated because some of his students published lecture notes they compiled from the courses he taught. Thus, the Course in General Linguistics, a foundational text for this field, came into being. I wonder if structuralism would have ever gotten off the ground if his students had been on their iPhones during class all semester...
Later theorists like Russian linguist Roman Jakobson and French anthropologist Claude Lévi-Strauss expanded the field of structuralism considerably, though they were strongly influenced by Saussure's theory of language. You could probably claim pretty safely that all contemporary theory stems from structuralism -- post-structuralism was largely a reaction to structuralism (as you might imagine), and that in turn was enormously influential in formulating the primary concerns of postmodern theory in its many forms.
So, my advice: pay attention to this part! Knowing about structuralism will make the later stuff seem a lot more comprehensible. I recommend going through the summary of each theorist's contributions to this field in the order they're listed on the drop-down menu, as they were often expanding upon one another's work in a way that will make more sense if read sequentially.
If you're feeling really ambitious, at the bottom of this page you will find a list of suggested reading that will clarify and flesh out the ideas introduced here. Go on -- give it a shot! Extra homework never killed anybody, that I know of...
Important Structuralist Theorists
Ferdinand de Saussure (1857-1913) - Swiss; considered the founder of structural linguistics and semiotics Roman Jakobson (1896-1982) - Russian; structural linguistics Claude Lévi-Strauss (1908-2009) - French; structural anthropology Roland Barthes (1915-1980) - French; semiotician (also considered a post-structuralist theorist)
Related Theoretical Fields
Formalism Russian Formalism New Criticism Post-Structuralism (a reaction to/against structuralism)