One of the most mysterious beliefs of Christians, both Catholic & most Protestant Christians, is the Holy Trinity. Just what do we mean when we say God exists in three persons as Father, Son, & Holy Spirit? This mystery has been discussed for 2,000 years and it even attributed to the Eastern Schism where the Eastern and Western Churches separated. To quote the Catholic Answers article on the Trinity:"The doctrine of the Trinity is encapsulated in Matthew 28:19, where Jesus instructs the apostles: '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.' The parallelism of the Father, the Son, and the Spirit is not unique to Matthew’s Gospel, but appears elsewhere in the New Testament (e.g., 2 Cor. 13:14, Heb. 9:14), as well as in the writings of the earliest Christians, who clearly understood them in the sense that we do today—that the Father, the Son, and the Spirit are three divine persons who are one divine being (God)."
There are many places in the Scriptures where the Father, Son, & Holy Spirit are mentioned in some way. But does that help most of us understand it? Probably not, but I'm sure we all still believe in the Trinity. We have to remember that believing in a mystery, which is what the Trinity is, does not mean that we are believing in something illogical. We are just believing in something that there is no possible way to understand completely, in this case it is God.
Jason Evert, host of several EWTN shows and also a Catholic author, explains how the Trinity can be one God in the following way: "All persons are beings, but not all beings are persons. For example, you are one being and one person. But a dog is one being and zero persons. With regard to the Trinity, there is one being, which is God, yet there are there Persons: Father, Son, and Holy Spirit. This is not illogical. If one were to say that there is one God and three Gods, or one Person and three Persons—that would be illogical. But one Being and three Persons is not a contradiction."
If you're like me, you probably still don't fully understand the Trinity, and that's perfectly ok! We, as human beings, don't have the full capacity to understand everything God puts before us; however, as Catholic Christians we still believe that there is a Trinity and that it is made up of God as the Father, Jesus as the Son, and the Holy Spirit.