Ideally, education is a transformative experience. Students should come away from a class different from when they entered it. One component of this difference is that their knowledge of a particular field of study is enhanced. Because of this, they should be better equipped to make connections between different areas of knowledge.
But apart from these outcomes, I believe that education should transform a student's general view of things, what the philosopher Ludwig Wittgenstein called our picture of the world. I don't mean by this that education should indoctrinate a student into a particular view on a particular subject but that by exposing them to many views on many subjects students gain a richer sense of the world they live in, how they are connected to it, and how they are an active participant in the world of ideas.
William James once said, "there can be no final truth in ethics any more than in physics until the last man has had his experience and said his say." I think that this is the fundamental purpose and benefit of education: to allow students to have their say by giving them the tools to think critically and to formulate their say.