A Bishop is an order in a number of churches, importantly the Roman Catholic church, the Eastern Orthodox church and Anglican church. Bishops are generally responsible for leading a large area (a diocese) and all the churches contained therein. An archbishop is a bishop in charge of an important diocese; however, an archbishop is not a higher rank. The Pope is also referred to as the Bishop of Rome.
Catholic, Anglican, and Eastern Orthodox bishops claim to be part of a continuous sequence of ordained bishops since the days of the apostles, the apostolic succession. The Catholic church, however, insists that Anglican orders are invalid, because of the rejection of transubstantiation. The Catholic church does however recognize as valid (though illegal) ordinations done by breakaway Catholic bishops, and groups descended from them, so long as the people receiving the ordination conform to other canonical requirements; this gives rise to the phenomena of episcopi vagantes.
Bishop, in Chess
A Bishop (see also Chess/Bishop) is a piece in the strategy board game of Chess. On both sides, there are two Bishops, each three spaces in from either side, between the Knight and the King or Queen. Each is referred to as the King's Bishop (Queen's Bishop), or more generally the white and black Bishops, as each resides on either a white or black square, and given its movement is only diagonal, it always remains on either the white or black square.
The Bishop has no restrictions in distance for each move, but is limited to diagonal movement, forward and backward. Bishops cannot jump over other pieces.
Strategically, Bishops are useful in that their diagonal movement allows them to attack or protect in broad strokes across the board. Placed toward the center of the board, or on either edge, a Bishop can restrict access to pieces that are forced to move one step at a time, block or protect a vulnerability for the King or "forking" an attack, by placing the piece in a position where both the opponent's Queen and Rook are under attack. Done correctly, this allows the Bishop to win a piece and disrupt the opponent's position.