A better question might be, "Which ending: the end of the autobiographical part at the end of Book IX? Or the very last page at the end of Book XIII?" This is a valid question, because there is some dispute over how the last four books fit into the work as a whole. (See R.S. Pine-Coffin's introduction to the Confessions for more on this issue.) But since Confessions exists in the form that it does, for us, the ending is the literal ending of the book.
And it's such a great finale that we're just going to quote the entire last paragraph here:
What man can teach another to understand the truth? What angel can teach it to an angel? What angel can teach it to a man? We must ask it of you, seek it in you; we must knock at your door. Only then shall we receive what we ask and find what we seek; only then will the door be opened to us. (XIII.38.3)
So Augustine chooses to end his work by talking about teaching. Which is fitting, since the entire narrative is really about his quest for knowledge. But he does something really fascinating in this last section as well.
First, he talks about teaching, and seems to conclude that it's actually not really possible to teach someone to understand something as fundamental as God (remember, "God" and "truth" are pretty much synonymous, as far as Augustine's concerned).
Then, because teaching isn't a viable option, he says we can only really learn about God by searching for him ourselves. But didn't Augustine write the Confessions to teach readers about God? Or is this book actually meant to show that people like Augustine, who wrote off Christianity for a long time before his conversion, need to come to a point where they themselves are receptive to the truth?
In the end, we think that the Confessions are not intended as a pedantic lecture about what people should believe. We think they're meant to demonstrate that change can only come on the individual level, when people are ready for it. Until then, we're all just knock, knock, knocking on heaven's door.