A bishop is the chief pastor and overseer of a diocese — a defined geographic area made up of a number of parishes. Bishops are understood to stand within apostolic succession, a historic line of ordination understood to trace back to the apostles, which is part of why the “historic Episcopate” is named specifically in the Lambeth Quadrilateral as part of the basis of Anglican identity.
In practice, a bishop's responsibilities include ordaining priests and deacons, confirming believers, guarding the doctrine and discipline of the church within the diocese, and representing the diocese at provincial and Communion-wide gatherings such as the Lambeth Conference. A diocese may also have one or more suffragan, or assistant, bishops supporting the diocesan bishop.
The senior bishop of a province — who presides over that province's other bishops — is usually called an archbishop or primate. How a person becomes a bishop varies by province: most involve election or appointment by a diocesan or provincial synod or an equivalent body, followed by consecration by other bishops, but the exact process differs across the Communion.