God is atrinityof persons: the Father, the Son, and theHoly Spirit. The Father is not the same person as the Son; the Son is not the same person as the Holy Spirit; and the Holy Spirit is not the same person as Father. They are not three gods and not three beings. They are three distinct persons; yet, they are all the one God. Each has a will, can speak, can love, etc., and these are demonstrations of personhood. They are in absolute perfect harmony consisting of one substance. They are coeternal, coequal, and copowerful. If any one of the three were removed, there would be no God. (See also, "Another Look at the Trinity")
Jesus, the Son, is one person with two natures: Divine and Human. This is called theHypostatic Union. TheHoly Spiritis also divine in nature and is self aware, the third person of the Trinity.
There is, though, an apparent separation of some functions among the members of the Godhead. For example, the Father chooses who will be saved (Eph. 1:4); the Son redeems them (Eph. 1:7); and the Holy Spirit seals them, (Eph. 1:13).
A further point of clarification is that God is not one person, the Father, with Jesus as a creation and the Holy Spirit as a force (Jehovah's Witnesses). Neither is He one person who took three consecutive forms, i.e., the Father, became the Son, who became the Holy Spirit. Nor is God the divine nature of the Son (where Jesus had a human nature perceived as the Son and a divine nature perceived as the Father (Oneness theology). Nor is the Trinity an office held by three separate Gods (Mormonism).
The word "person" is used to describe the three members of the Godhead because the word "person" is appropriate. A person is self aware, can speak, love, hate, say "you," "yours," "me," "mine," etc. Each of the three persons in the Trinity demonstrate these qualities.
The chart below should help you to see how the doctrine of the Trinity is systematically derived from Scripture. The list is not exhaustive, only illustrative.
The first step is to establish the biblical doctrine that there is only one God. Then, you find that each of the persons is called God, each creates, each was involved in Jesus' resurrection, each indwells, etc. Therefore, God is one, but the one God is in three simultaneous persons. Please note that the idea of a composite unity is not a foreign concept to the Bible; after all, man and wife are said to be one flesh. The idea of a composite unity of persons is spoken of by God in Genesis (Gen. 2:24).
Therefore, the doctrine of the Trinity is arrived at by looking at the whole of scripture, not in a single verse. It is the doctrine that there is only one God, not three, and that the one God exists in three persons: Father, the Son, and the Holy Spirit. An analogy would be time. Time is past, present, and future. But, there are not three times, only one.