Gamepoints are representative of the number of simultaneous games you can have running at any one time. A 9x9 board is 1 point, a 13x13 board is 2 points, and a 19x19 board is 4 points. These points are returned upon completion of a game and can then be used on more games.
This limitation is designed to help limit the load that boards put on the server, thus not going over the bandwidth limitations or stressing out the processor on the shared server.
As the administrators wish to encourage competitive play on this site, all tournament and minitournament games do not count towards your gamepoint limit.
With the introduction of title tournaments, players are given an extra 32 gamepoints for each title they hold whilst they hold the title.