In Sacred Scripture, the Holy Spirit is called by different names: Gift, Lord, Spirit of God, Spirit of Truth and Paraclete, among others. Each of these words indicates something to us about the Third Person of the Holy Trinity.
It is "Gift", because the Father and the Son send it to us freely: the Spirit has come to dwell in our hearts; He came to always stay with humanity. Furthermore, from Him proceeds all graces and gifts, the greatest of which is eternal life together with the other divine Persons: in Him we have access to the Father through the Son. The Spirit is "Lord" and "Spirit of God", which in Sacred Scripture are names that are attributed only to God, because he is God with the Father and the Son. It is the "Spirit of Truth" because it fully teaches us all that Christ has revealed to us, and guides and maintains the Church in the truth. He is the "other" Paraclete (Comforter, Advocate) promised by Christ, who is the first Paraclete.
The Holy Spirit intimately unites the faithful with Christ so that they form a single body, the Church, where there is a diversity of members and functions.