Synodic comes from the Latin word synod meaning "meeting" so the moon has to "meet" with the sun every new moon. A synodic month takes 29 1/2 days A Sidereal month takes only about 27 & 1/3 days,...
A sidereal month is the time it takes the moon to complete one orbit of earth. A synodic month is longer than a sidereal month because it takes longer for the moon to go through it's phases