The following is the general description of what council/session is from the Presbyterian Book of Order
The session of a particular church consists of the pastor or co-pastors, the associate pastors, and the elders in active service. All members of the session, including the pastor, copastors, and associate pastors, are entitled to vote.
The session is responsible for the mission and government of the particular church. It therefore has the responsibility and power to provide opportunities for evangelism to be learned and practiced in and by the church, that members may be better equipped to articulate their faith, to witness in word and deed to the saving grace of Jesus Christ, and to invite persons into a new life in Christ; to receive members into the church upon profession of faith upon reaffirmation of faith in Jesus Christ, or upon satisfactory certification of transfer of church membership, provided that membership shall not be denied any person because of race, economic or social circumstances, or any other reason not related to profession of faith; to lead the congregation in participation in the mission of the whole Church in the world; to provide for the worship of the people of God, including the preaching of the Word, the sharing of the Sacraments, and for the music program, in keeping with the principles in the Directory for Worship, and to appeal to the presbytery for a duly trained and authorized elder under the provisions of G-11.0103 in those extenuating circumstances where an ordained minister of the Word and Sacrament is not available to meet the needs for the administration of the Lord's Supper; to provide for the growth of its members and for their equipment for ministry through personal and pastoral care, educational programs including the church school, sharing in fellowship and mutual support, and opportunities for witness and service in the world; to develop and supervise the church school and the educational program of the church; to lead the congregation in ministries of personal and social healing and reconciliation in the communities in which the church lives and bears its witness; to challenge the people of God with the privilege of responsible Christian stewardship of money and time and talents, developing effective ways for encouraging and gathering the offerings of the people and assuring that all offerings are distributed to the objects toward which they were contributed; to establish the annual budget, determine the distribution of the church's benevolences, and order offerings for Christian purposes, providing full information to the congregation of its decisions in such matters; to lead the congregation continually to discover what God is doing in the world and to plan for change, renewal, and reformation under the Word of God; to engage in a process for education and mutual growth of the members of the session; to instruct, examine, ordain, install, and welcome into common ministry elders and deacons on their election by the congregation and to inquire into their faithfulness in fulfilling their responsibilities; to delegate and to supervise the work of the board of deacons and the board of trustees and all other organizations and task forces within the congregation, providing for support, report, review, and control; to provide for the administration of the program of the church, including employment of nonordained staff, with concern for equal employment opportunity, fair employment practices, personnel policies, and the annual review of the adequacy of compensation for all staff, including all employees; to provide for the management of the property of the church, including determination of the appropriate use of church buildings and facilities, and to obtain property and liability insurance coverage to protect the facilities, programs, and officers, including members of the session, staff, board of trustees, and deacons; to maintain regular and continuing relationship to the higher governing bodies of the church, including:
(1) electing commissioners to presbyteryd and receiving their reports; sessions are encouraged to elect commissioners to the presbytery for at least one year, preferably two or three;
(2) nominating to presbytery elders who may be considered for election to synod or General Assembly;
(3) in both the above responsibilities, implementing the principles of participation and inclusiveness to ensure fair representation in the decision making of the church;
(4) observing and carrying out the instructions of the higher governing bodies consistent with the Constitution of the Presbyterian Church (U.S.A.);
(5) welcoming representatives of the presbytery on the occasions of their visits;
(6) proposing to the presbytery and, through it, to the synod and the General Assembly such measures as may be of common concern to the mission of the whole church;
(7) sending annually to the stated clerk of the presbytery statistical and other information according to the requirements of the presbytery.
To establish and maintain those ecumenical relationships necessary for the life and mission of the church in its locality; to serve in judicial matters in accordance with the Rules of Discipline; to keep an accurate roll of the membership of the church, in accordance with G-10.0302, and to grant certificates of transfer to other churches, which when issued for parents shall include the names of their children specifying whether they have been baptized, and which when issued for an elder or deacon shall include the record of ordination.