The Holy Ghost is also referred to as the Holy Spirit, the Spirit of God, the Spirit, Spirit of the Lord, and the Comforter. I tend to usually say the Spirit.
The Spirit's main purpose is to testify that Jesus is the Christ. He has other roles, such as comforting us. He also inspires us and guides us. Basically, the Spirit is how the Savior reaches out to us as He would do if He were with us on earth today.