According to the Christian
Trinity, God is in three parts; God the Father, God the Son, and God the Holy Spirit. When one makes the
sign of the cross on their chest, the Holy Spirit is the part where they touch their shoulders. It was formerly and still is also known as the
Holy Ghost or
Sancte Spiritus
Christians believe (from the Bible) that when Jesus forecasted his death and resurrection, he said that he would have to leave his followers for a while, but that the Holy Spirit would come. This is known as the Pentecost.
"On the day of Pentecost all the Lord's followers were together in one place. Suddenly there was a noise from heaven like the sound of a mighty wind! It filled the home where they were meeting. Then they saw what looked like fiery tongues moving in all directions, and a tongue came and settled on each person there. The Holy Spirit took control of everyone, and they began speaking whatever language the spirit let them speak." (Acts,2:1-6)
From that day on, each of the apostles was guided by the Holy Spirit. It has no body, but is considered God Himself in a spiritual form. God fills their mind and guides them. In the bible, each of the apostles was then guided by God to perform miracles as
Jesus had done, and lost their fear of death.
The Sacrament of Confirmation is supposed to fill the receiver with the Holy Spirit. It's how God influences things on Earth, since He has ceased to speak to Man.
Catholics believe that since Jesus passed down the Holy Spirit to his Apostles, they in turn "recruited" others, which since then lets bishops ordain priests with the power of the Holy Spirit. The Holy Spirit is the force that allows Transsubstantiation, where the Wine turns into the Blood of Jesus and the bread into His body. When the priest holds it up and the bell rings, the Holy Spirit is supposedly there and performing the miracle. According to the Nicene Creed, the Holy Spirit proceeds from both The Father and The Son. Such is the belief the Catholic faith demands.
Also, the Holy Spirit is what "inspired" the authors of the Bible and guided them with what to write. It is said that God would never let any of them make a mistake in such important words, so the Holy Spirit must have been present.
The Holy Spirit is supposed to be "mysterious" in the Trinity. It's said by priests that God and Jesus' love for mankind was so fantastically great that it spawned a third, the Holy Spirit is a result of all the coalesced love, and sets people in the right direction.
All Christians believe in it, regardless of denomination. Baptists make a big show of when they feel the Holy Spirit has filled their hearts from their faith, Evangelical ones will jump up and down saying Halleleujiah in church loudly. Catholics believe that the Pope takes his guidance from the Holy Spirit. He can't communicate with God directly, and Jesus isn't back yet, so the Holy Spirit leads him into making decisions. The Holy Spirit must guide him, as God would never let the Pope mislead His followers against what God wants.
For a better definition, ask your local priest or minister, as there is some difference in interpretation.
Also, check out the Catholic Encyclopedia's entry: http://www.newadvent.org/cathen/07409a.htm
Christians, beware! Don't just get up and bad-mouth the Holy Spirit!
"I tell you that any sinful thing you do or say can be forgiven. Even if you speak against the Son of Man, you can be forgiven. But if you speak against the Holy Spirit, you can never be forgiven, either in this life or in the life to come." -Attributed to Jesus, New Testament book of Matthew
Some interpret that as you should never ever badmouth that part of the trinity. Others say that since God is not going to punish anybody except those who deliberately sin against their conscience, then this expresses that ideology.
Interestingly enough, Muslims believe in a Holy Spirit "Ruh Quddus" but he is clearly defined in the Quran as the angel Gabriel (pbuh) and not part of nor God.