Literary theory can be defined simply as the various methods we use to analyze and understand literature. In other words, when we try to understand literature, we use certain methods to help us understand the meaning, and those methods comprise literary theory. Literary criticism, on the other hand, is the practical application of those theories or methods to particular works of literature--the actual use of a method to better understand a text's meaning.
Literary theories include formalism, historicism, deconstructionism, gender approaches, psychological approaches, and several other methods critics and readers use to understand meaning. For example, if a reader wants to understand every element of Nathanial Hawthorne's short story "Young Goodman Brown," who has a dream that changes his entire outlook on his family and society, a critic using the historical theory of criticism might look at the Puritan belief system in order to see what elements of Puritanism appear in the story and affect the story's outcome. Using biographical theory, which postulates that an author's life may affect the way he or she writes, a biographical approach would require the critic to look for any evidence in Hawthorne's life that he felt negatively about Puritanism. Such an approach would discover, for example, that Hawthorne actually changed his last name, which was originally spelled without the w, because he was appalled that one of his ancestors was a judge at the Salem witch trials in 1692-93.
In sum, then, theories provide the methods by which readers and critics look at the meaning of literature, and criticism is the use of those methods to understand meaning.