The Incarnation of Christ means that we profess that God has become human without ceasing to be God. These teachings can be summarized in the following points:
Incarnation
Read the Catechism of the Catholic Church, #422-570
Atonement
Read the Catechism of the Catholic Church, #571-667
Here's Jon Stotts' take on why Jesus had to die.
As with all Catholic teachings, the mystery of the cross isn't just a theory -- it's a reality that we must live and pray. One of the most widely used Catholic methods of contemplating the paschal mystery is the rosary, a form of prayer that uses several distinct vocal prayers to lead us into a period of quiet meditation. Learn how to pray the rosary here or here. Read more about the spirituality of the rosary here. Need a rosary? Head to St. Mary's Bookstore downtown. It's a little tough to get started with this prayer form, but once you figure it out, you'll have a time-tested means of entering into communion with God whenever you have a couple of minutes to spare.
Becoming a Catholic is about responding to God with your whole life in union with others who are responding with their whole lives. Two millenia ago, God took on the full life of a human man; in doing this, God invites us to take on the life of the Triune God. We are about Jesus Christ: He is the center of everything that we do, say, and believe. We are his people, we accept that he is trustworthy and we believe that his is the way to true and lasting happiness.