Baptism makes us adopted sons and daughters of God. Christ is the only begotten Son of God. So while our sonship is not the same as his, it is still a participation in that sonship. We are not God; but Jesus himself described our sonship by saying, "[Y]ou are gods" (Jn 10:34). His Sonship is uncreated and eternal. Ours is a grace; it is created and adoptive. But it is real. In the supernatural order as in the natural order, adoptive children are real children who enjoy the real paternity of their adoptive fathers.
What we receive by grace, however, is greater still than the gift we receive from our parents. Through baptism, we are more truly God's children than we are children of our earthly parents. Through baptism, we are more truly at home in heaven than in the place where we grew up. Saint Maximus Confessor said that we "become completely whatever God is, save at the level of being", and we receive for ourselves "the whole of God himself", in all his infinity, in all his eternity.
The Trinitarian formula is what Jesus commands the apostles to use when they baptize: "Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit" (Matt. 28:19).
More specifically, anybody even an atheist can administer baptism if he has the proper intention. According to the Catechism of the Catholic Church (CCC 1256) "the intention required is to will to do what the Church does when she baptizes, and to apply the Trinitarian baptismal formula." The reason anybody can baptize is that it is, in fact, Jesus Christ who performs the baptism.
Therefore, since baptism is performed by Jesus and the baptismal formula is provided by Jesus in scripture and confirmed by Tradition and the church, getting it right matters.