Your open positions are the trades you have made that are still able to incur a profit or a loss. When a position is closed, all profits and losses are realised and the trade is no longer active.
To close an open position, you usually need to reverse the trade made to open it (selling any assets that have been bought, or vice versa). Alternatively, this can happen automatically if a position reaches its expiry date or has a stop or a limit in place which is subsequently filled.
There are some exceptions to this, as some trades will always run until their expiry and cannot be closed by the trader, and some trades have no expiry.