In the Catholic Church: The College of Bishops, headed by the Pope, is considered the supreme authority in the Church. It's understood as having both an ordinary and an extraordinary magisterium (teaching authority). The ordinary magisterium is exercised daily by the bishops in their respective dioceses, while the extraordinary magisterium is exercised collectively, usually through an ecumenical council or a papal pronouncement. The College of Bishops' authority is considered to stem from the apostolic succession, tracing back to the Apostles.
In other Churches: Other churches, particularly those with an episcopal structure (meaning they have bishops), may also use the term "College of Bishops," though the meaning and power may differ significantly from the Catholic understanding. In some denominations, the college might be primarily an advisory or administrative body, while in others it might have more significant decision-making powers. The concept of apostolic succession may not be as central in these other churches.
Therefore, to understand the exact meaning of "College of Bishops," it's crucial to know the specific Christian denomination being discussed.