When it was first released it's description on the Jagex site was:
Place counters to try to control as much of the board as possible. Trap your oppoenents pieces to capture them! Part of the Castle-GamesDomain multiplayer games suite.
Objective of Reversi
To win this game you must have more counters of your colour on the board at the end of your game than the opponent.
How to play
You must take it in turns to place counters of your colour on the grid. A counter can only placed adjacent to a counter of the opposite colour, and by placing the counter you must capture at least 1 piece. If there are no possible moves, then the other player gets another go. The game ends when neither player can move, and the player with most counters on the board wins.
If when you place a piece on the grid it traps 1 or more enemy pieces, (i.e. the row of enemy pieces has one of your pieces at one end, and the piece you just placed at the other.) Then the entire row of trapped pieces is captured and converted to your colour. It is possible to capture multiple rows simultaneously, but you can only capture pieces in a straight line. For this reason edge squares are more valuable as they are harder to capture, and corner squares are especially valuable as they are impossible to capture!