As I see it, theory is a way for us to move past reading one literary work after another in terms of the author's life (to what extent is the work autobiographical) or some supposedly universal moral truth (what can the work teach all of us about life). Theory offers new perspectives and systematic ways of uncovering new meanings.
A structuralist approach often looks very closely at the sequence of events in a story and then explores whether or not the pattern within that story matches the trend among similar stories. Vladimir Propp's analysis of fairy tales (see his Morphology of the Folk Tale) is a very good example; Propp identifies common elements among fairy tales, such as "absention" (a character leaves the safety of home) and "interdiction" (a character is told what to do or not to do, such as "Don't go into the woods" or "Stay on the path"). Think "Little Red Riding Hood" or The Wizard of Oz.
A post-colonial approach, by contrast, often looks very closely at the distribution of power, the granting or denial of agency, the often subtle but hugely important relationships between urban centers and far more remote areas, and related topics. The English language and the teaching of Shakespeare in India are not inherently neutral subjects, for example; they are the legacy of centuries of British occupation of that country. Sometimes these relationships are pretty obvious (see, for example, The Hunger Games), but sometimes they are very subtle and easily overlooked. The world within Jane Austen's Mansfield Park is built on the whole system of British colonialism, but the far-away sugar plantation receives only a few brief mentions in the novel.
Thus, theory informs literary criticism. A particularly theory often encourages the reader to ask questions about a literary work that might not otherwise be asked or linger over small but significant details in the work that might otherwise be passed over by a casual reader.