Sometimes referred to as full guard. The closed guard is the typical guard position. The legs are hooked behind the back of the opponent, preventing them from standing up or moving away. The opponent needs to open the legs up to be able to improve positioning. The bottom combatant might transition between the open and closed guard, as the open guard allows for better movement, but also increased risk in the opponent passing the guard.
The guard game is one of the major differences between BJJ and Judo competition. In judo the guard is rarely played (mostly due to referee stoppage) or due to the fact that once judo players get to this position they cease to attack therefore the referee will stop the fight.
There are endless options from within a closed guard but i decided to add in a video of a basic gaurd pass.