Grammatically, "our" qualifies a reality common to more than one person. There is only one God, and he is recognized as Father by those who, through faith in his only Son, are reborn of him by water and the Spirit. The Church is this new communion of God and men. United with the only Son, who has become "the firstborn among many brethren," she is in communion with one and the same Father in one and the same Holy Spirit. In praying "our" Father, each of the baptized is praying in this communion: "The company of those who believed were of one heart and soul."
Source: Catechism of the Catholic Church (Vatican.va)