A Game Board (ゲーム盤 Gēmu-ban) is a setting defined by a set of characters (pieces) who act according to predefined rules, and two or more key characters (players) who try to influence the events that take place to gain their desired outcomes.
Ryukishi07 has said that the When They Cry series is based around "pieces moving on the gameboard and a player that observes them and tries to find out the rules of the game. Each piece on a gameboard has its own winning conditions and moves by its own rules. These pieces meet, interfere with each other, some invisible from the first glance chemistry borne between them. By actions that these pieces take in those situations you can understand the rules, and that world-view is a fundamental rule of When They Cry."
Game boards can be seen as a specific set of Fragments centered around a single location. While game boards can have infinite, random variables affecting the events within, there are Rules (X, Y and Z) that are consistent. Discovering these rules and overcoming them is the key to winning game boards.
Game Boards in Umineko
Umineko no Naku Koro ni uses the concept of game boards and pieces in a literal context, as the mystery on Rokkenjima is presented as a game played between beings on a higher dimension, the Meta-World.
Pieces in Umineko have a meta-world counterpart that controls their piece counterpart, however this only applies to magical characters such as witches, demons and the like. Most Human pieces only exist on the game board and are controlled by the Game Master whenever appropriate. While Battler himself exists in the meta-world, the level of control he has over his piece counterpart is unclear.
It is also said that pieces can only do things possible for their original selves and act according to their original personality, however no example of a piece "disobeying" their original self has ever been shown. Furthermore, the existence of Black Battler shows that even a person as kind-hearted as Battler can be made into a cruel piece.
Game boards in Umineko also involve the usage of Red Truth, which is used to declare factual information. If the Game Master is not careful with their Red Truths and end up contradicting the story, then Logic Errors are created. The Game Master or pieces involved will become trapped until they can solve the error.