The Catholic faith has many uses of the word "father".
First, we often think of God the Father. He is our Creator and as such we are all His children. From the beginning He has taught us to be like Him and how to be good people. Like a parent teaches and molds their child, so God teaches and molds us. He does this first through his Law and the prophets in the Old Testament and then leads a perfect example through Jesus in the New Testament. Jesus taught us how to please the Father, love the Father and pray to the Father.
We also immediately think of our own father when we hear the word father. Our fathers are our biological and earthly fathers. They care for, nurture and protect us as we grow up. We are God's gifts to our parents who pass on the faith and Jesus' teachings to us.
Another common use of the word Father is the name we use for priests. Of course we do not mean this literally or as a replacement for the term we call God. When we call our priests "father" it is in reference to a spiritual father like how the early Christians viewed the first Christian teachers such as Peter, Paul and John. In fact many of their letters we read in the Bible address the Christians as "my children". The priests today do the same: they lead us closer to Christ as a parent leads a child to safety. They teach us to remain in God's grace the way a parent teaches a child right from wrong.
Thank you God the Father for our fathers and our fatherly priests!