The Wednesday Audience is a papal tradition that stretches back to the 19th century. Initially popes used it as a means to meet with pilgrims who came to visit them at the Vatican and to offer an occasional teaching, but John Paul II transformed these events into ongoing catechetical addresses, in which he would take dozens or even hundreds of Wednesday audiences to teach on a particular doctrine of the Church. The well-known Theology of the Body, for instance, is from Wednesday audiences over the course of four years in the early 1980's. Pope Benedict XVI has taken up the same tradition in his pontificate. He began by finishing the series of addresses on the Psalms and Canticles that John Paul was giving before he died, typically taking the text that John Paul had written and making some personal changes. After that, however, Benedict began offering Wednesday audience catechetical addresses which are truly his own, in the sense that they are his own writings. He began with a series on the Church and the Apostles, which have since been compiled and published both by Our Sunday Visitor and Ignatius Press (contact the Evangelization & Catechesis office at the links to the lower left for more information on these books). He has since moved on to the Fathers of the Church, those theologians who wrote in the first centuries of Christianity.
You can find all of these addresses at the Vatican website, but for your convenience they will also be linked here in the near future.