Awhile back when I was looking online regarding the number three as used in Scripture, I found Thoughts on the number three, by Vernon Johnson of Denton Primitive Baptist Church. I think it is quite interesting.
"In the Old Testament there were three buildings that when completed were made manifest by a cloud filling and surrounding the building, in which it was said, 'the glory of the Lord filled the building.' These three buildings were the tabernacle in the wilderness, the temple built in Solomon’s day, and the building of Ezekiel’s vision. Similarly, three times in the book of Acts we read about the baptism of the Holy Ghost. First, on the day of Pentecost the Spirit filled the house where the church was gathered at Jerusalem. Next in the city of Samaria (Acts chapter 8) when the apostles came down and laid their hands on the people they were filled with the Holy Ghost. Finally, at the house of Cornelius when Peter preached unto the Gentiles the Gentiles were baptized with the Holy Ghost (Acts 11:15, 16).
"When someone comes seeking entry into the church, they enter thru water baptism. Water baptism signifies three things: the death, the burial, and the resurrection of the Lord Jesus Christ. When someone is baptized he is baptized in the name of the Father, the Son and the Holy Ghost.
"The worship service of the true church is composed of three parts: singing, prayer, and preaching. Likewise, the communion service as laid down for us in the scriptures consists of three parts:
"1. Eating the unleavened bread which signifies the pure, perfect, sinless body of Christ.
"2. Drinking the wine which signifies the blood of Christ which he shed to redeem us from our sins.
"3. Washing the disciples feet which signifies the humility required to serve one another and thus serve the Lord.
"In our worship service we are told to sing and make melody in our hearts unto the Lord. Singing consists of three parts: melody, harmony and rhythm. Similarly when we pray, we pray with the unction and leadership of the Holy Spirit; we pray in the name or authority of Jesus Christ, who intercedes for us; and we pray unto the Father." -- From Glad Tidings, Nov/Dec 2002