In fencing, a disengage is an evasion of your opponent's attempted parry-- you are counting on your opponent to try to stop your original attack.  You deftly move around their blade and switch your attack to a different line than the one originally established.

It should ideally be as small a motion as possible, moving the point of your blade in a half-circle around your opponent's bell guard and into a different line of attack.  If your blade touches your opponent's guard while executing the movement, it is not considered a successful disengagement.  If you bring your arm back towards you during the movement, that is also not considered a successful disengagement (by bringing your arm backwards towards your body, your original attack is stopped and your second attack to the new line is considered a remise).

It is a particularly effective move when fencing beginners, who generally only expect attacks into their main line (their upper inside line, the 4 line).