The word Trinity cannot be found in the Bible, but the truth of it can. While there's only one God, the Godhead consists of three distinct persons - the Father, Son, and Holy Spirit. All are equally omniscient, omnipotent, omnipresent, eternal, and unchanging, but each one has unique functions.
Scripture shows how each member of the Trinity fulfills His specific role, and it also reveals how those three roles interrelate. Let me express this idea in simple terms: The Father creates a plan, Jesus Christ implements the plan, and the Holy Spirit administers the plan.
The way of redemption showcases these roles in a clear manner. The Father designed and organized how mankind would be redeemed (Galatians 4:4-5). He set into motion a complex set of events, actions, and prophecies which culminated in the life and death of a Savior. The Son carried out the plan (John 6:37-38). He followed the Father's instructions to come to earth, even though that meant He would have to die. The Holy Spirit sees to it that every person feels a call toward God's saving grace (John 14:26, 16:8; Romans 1:19-20). Furthermore, He transforms the lives and hearts of those who receive salvation through Jesus Christ.
The Father, Son, and Spirit are equal in their divine attributes. Yet each relates to mankind in a different way because He has a specific role. It's very important to understand this distinction: We do not have three gods; we have one God in three persons functioning uniquely and perfectly.