As Orthodox, we believe that the apostles granted the Sacrament of the laying of the hands after Baptism so that the baptized receive the Holy Spirit to dwell inside of them (Acts 9:2-6). The apostles, Church Fathers, and their successors the Bishops, later established anointing by the Myron Oil as an alternative for laying hands for the indwelling of the Holy Spirit. Since the priest and parishioners have the Holy Spirit dwelling inside of them already, why do we call down the Holy Spirit to participate in Church rites if He is already present?
Every time we receive the Holy Spirit, we receive a certain grace. For example, when the Lord breathed in the face of His disciples after His resurrection, He gave them the grace of the priesthood. In the priesthood, the same priest receives another grace and so on. What differentiates our priests from pastors of other denominations is the invocation of the Holy Spirit during the rites of the ordination of the priest. Thereafter, the priest is endowed with the authority to administer all the holy sacraments.
This gift is not given to everyone but to whom the bishop or pope ordains. This is because the bishop or patriarch received this grace from the Holy Spirit directly from the successors of the apostles who received it from our Lord Jesus Christ.
When the Holy Spirit descended like tongues of fire, this was for preaching. In the same way, in marriage, we receive the grace of oneness and unity. The Holy Mystery of Matrimony spiritually unites two persons into one through the invocation of the Holy Spirit. The Holy Spirit dwells in and works through the believers and gives each one different gifts for diverse ministries. Without the invocation of the Holy Spirit upon the Bread and Wine during the Divine Liturgy, these elements would remain just bread and wine and not become the holy Body and Blood of our Lord Jesus Christ. It is clear that all the rites and the Holy Mysteries of the Church implore the invocation of the Holy Spirit. Through His participation in the rites and prayers of the Church, elements upon which He is invoked mysteriously change and are elevated into the spiritual matter according to the prayers and supplications of the priest.
"There are diversities of gifts, but the same Spirit. There are differences of ministries, but the same Lord. And there are diversities of activities, but it is the same God who works all in all. But the manifestation of the Spirit is given to each one for the profit of all: for to one is given the word of wisdom through the Spirit, to another the word of knowledge through the same Spirit, to another faith by the same Spirit, to another gifts of healings by the same Spirit, to another the working of miracles, to another prophecy, to another discerning of spirits, to another different kinds of tongues, to another the interpretation of tongues. But one and the same Spirit works all these things, distributing to each one individually as He wills" (1 Corinthians 12:4-11).