In literary theory, a structure is a general term. It can refer to linguistic structure: grammar and syntax. It can refer to the structure of how signifiers (words, written and said) refer to signifieds (meanings). The word "bear" means the thing or idea of a bear. Structure can also refer to how cultural structures inform a literary work.
There are structures in culture (religion, marriage and relationships, myths, economic structures and relationships, social bonds, etc.). One could bring in Freud, Marx, or Levi-Strauss to analyze how psychoanalysis, class struggle, or familial traditions inform the structure of a novel. In short, we make and use structures to make sense of things, both in life and in literature. Structures determine how we behave, communicate, interact, and interpret.
But what is a structure? Here are some examples. The relationship between the word "bear" and the thing/idea is a structural relationship. The structure of society is based upon economic exchange, marriages, unequal wealth distribution, and colonial/post-colonial struggle. Typically, dramatic structure is made up of the exposition, rising action, climax, falling action, and the resolution. And the plot or themes of a dramatic work might be based upon a grand narrative or system of beliefs. This could be one thing or a combination of things like Western thought, ethics, progressive politics, social democracy, and so on. Binary oppositions also structure the way we think: good/evil, man/woman, inside/outside, and rich/poor.
One could analyze Hamlet and conclude that it is built upon a typical dramatic structure with a revenge plot. And thematically, it is based on traditional Western notions of good and evil. Because of the complex relationships with mother, father, and uncle, it is ripe for psychoanalytic analysis which might reveal other mythological and cultural influences and structures: the reluctant hero, Oedipus, and more. To analyze Hamlet and conclude with a "stable center" is to give it a unified meaning. And a structuralist might argue that a complete structural analysis of the play would give us a universal, unified meaning. In other words, the structural center of a work is the one meaning that is the best. The center holds because all of the structural analyses work together.
Post-structuralists and deconstructionists eventually came along and took such notions apart. They argue that while structures are real, they are constructs: made up. They try to show how a center is actually unstable by deconstructing themes, language, and cultural assumptions.
Structuralists attempt to show how cultural, linguistic, and other structures give a literary work meaning. Post-structuralists attempt to show how these structures can be undermined, contradicted, or abandoned in favor of a more open analysis based upon free play and multiple interpretations.