Each player's goal is to connect their two opposite sides of the board, by colouring a chain of adjacent cells with their colour. Players take turns colouring any empty cell, starting with red. Once coloured, a cell can't be changed. The game ends when one player successfully connects their sides.
In Hex, the first player always has an advantage. To balance this, the second player (blue) can choose to use their first move to "steal" red's first move. If blue chooses to use the swap rule, the first red cell is replaced with a blue cell in the corresponding location for blue, that is, the cell "reflected" across the long diagonal.