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Boxes is normally played on paper, and since it's been around a while - and played in many different Math classes - there's more than a few variations and names for it. The one presented here is the version that kept me occupied during classes.
This is a game for 2 players, each taking it in turn to connect two adjacent dots (not diagonally) on a grid of dots.
By completing a square (drawing the fourth line around a cell) that player claims that box and takes another turn. Otherwise, your turn ends after making a move which doesn't complete a square.
The winner is the player who has claimed the most boxes at the end.
More information about Boxes can be found, for example, by searching AltaVista. Some suggested strategies are also available online if you wish to make a computer opponent.
I would normally provide some graphics to get you started, but this game isn't very graphical. You just need to represent dots, selected dots, lines (of both players if you wish) and marked squares.
Likewise, a demonstration board is unnecessary - it's just a grid of dots, of whatever size you want - an 8 by 8 grid makes for a quick game, while 20 by 20 takes a long time to get going.
Games are distributed under the WebGames License