Structuralism is a movement that goes back to the work of Ferdinand de Sausssure, the great linguist. The basic idea is that things (things can be anything) are part of a structure. So, words, in order to have meaning, have a structure. Or if one is studying myths, these myths, too, are part of a larger structure. In this way, the application of structuralism can be almost limitless - sociology, classics and anthropology come to mind. Structuralism is, in some ways, a study of part to whole.
So, when we come to literature, the point is that texts also have an underlying structure. To find this structure will be to find the meaning of the text. Also structuralism likes to see things through binaries. This should not surprise us, because, if there are structures, then there will probably also be binaries. Levi-Strauss is probably the one who is associated with this line of thinking most. Finally, it should be stated that literary approaches to structuralism are not without critics. Anything too neat is probably understating the problems and difficulties of life in the real world.
Structuralism is a literary movement utilizing the methods of structural linguistics (system of language) and structural anthropology (system of culture as it provides meaning to literary works). Structural literary critics do not seek actual explication or analysis of unique texts but an account of the modes of literary discourse and their operation. There are two basic types of structuralism. One concentrates its study on the patterns formed by linguistic elements in a work in order to find which ones unify the text and throw certain elements in relief. More common, however, is the type which looks at literary conventions as a system of codes that contribute to and convey meaning. However, both types focus on the framework of a piece of literature to point to meaning within the entire work (punctuation patterns, patterns in speech, word choice, etc).