The New Catholic Encyclopedia gives this definition:
Originally a mathematical term, the Greek word for analogy means “proportion” and was borrowed by philosophers to refer to the relationship between concepts of things that are partly the same and partly different. It took on special importance in the concept of analogy of being (Latin: analogia entis). The analogy of faith (analogia fidei) must not be confused with this more philosophic concept..
The phrase analogy of faith is biblical: Romans 12:6 speaks of the charism of prophecy, along with such similar gifts as ministering, teaching, exhorting. Prophets exercised one of several “offices” within the primitive church (Acts 11:27 13:1); guided by the Spirit, they gained insight into the faith or recognized tasks to be undertaken. The Pauline injunction is given that this gift of prophecy must be exercised “according to the proportion (Gk. analogian) of faith.” No prophet is to be accepted who proclaims anything opposed to the “one faith” proper to the “one body in Christ.” Such preaching would be out of proportion to, or beyond, the objective truth entrusted to the Christian community.
The analogy of faith, therefore, has always been associated with the one unchanging faith of the Church; it is closely related to the notion of Tradition and soon became a norm for the early Christian writers. They saw a “proportion” in the manner in which the New Testament complements the Old Testament and in which each particular truth contributes to the inner unity of the entire Christian revelation.
Thus the phrase came to indicate a rule or guide for the exegesis of Scripture. In difficult texts, the teachings of tradition and the analogy of faith must lead the way. The Catholic exegete, conscious of his faith, recognizes the intimate relationship between Scripture and Tradition; he strives to explain Scriptural passages in such a way that the sacred writers will not be set in opposition to one another or to the faith and teaching of the Church.