I heard a Catholic Bishop talking about William of Ockham (Robert Barron) but I'm still not quite sure of some things: What is the contribution of William of Ockham to the Church? What would sum up his work? And how does it help us today? Also (for Catholics) how is he seen in the Catholic Church today?
William of Ockham was a Franciscan Friar who lived near the end of the medieval era, shortly after the life of St. Thomas Aquinas. His biggest contribution to philosophy is in the area of metaphysics, with his invention of nominalism: the rejection of the existence of universals. You can read about this metaphysical theory on the Stanford Encyclopedia of Philosophy.
The rejection of the reality of universals undermines the metaphysical framework used by Thomists, who follow in the scholastic tradition (though Ockham was also a scholastic, himself) and accept Aristotle's metaphysical premises, and offers an alternative framework for theological work. Nominalism is closely associated with the prioritization of the will. William, like his contemporary Franciscan Bl. John Duns Scotus, thought that God willed first, and then understood, as a matter of logical ordering. Whereas, Aquinas would say that God first understood and then created. William of Ockham's nominalism follows from Scotus' prioritization of God's will. If God first willed and then understood, then there are no universals according to which God creates. He simply wills, and then abstracts and names things.
It should be clarified that none of these men believed that God knew and then willed nor that He willed and then knew as a matter of temporal causality, or really of causality of any kind. This was a logical ordering only.
Back to William, his thought along with Scotus' is foundational to the classical Franciscan theological approach. It can be contrasted with the classical Dominican theological approach, commonly called "Thomism," named after St. Thomas Aquinas. Many Thomists blame nominalism for a number of modern philosophical errors.
As for his theological contributions, William held to a form of fideism, which is generally understood to be a rejection of reason as playing a real role in the Christian acceptance of revelation. William rejected logical demonstrations of Catholic Truths, and instead held to the teachings of the Church by faith alone. This is not a doctrine of salvation, as the Protestant doctrine of faith alone is, but a doctrine regarding how Christian Truths are to be beleived. William says they can only be accepted on faith-based grounds, and not by reason. This can again be contrasted with Thomism, which accepts revelation on faith as a starting point for theology, but builds arguments using reason from there to answer speculative and moral questions. For example, William would say that we must take on faith not only the doctrine of the Trinity (Thomas would agree), but also the claim that the Holy Spirit proceeds from the Father and the Son (for which Thomas offers a logical argument).