A crossover is a type of filtering system that permits only certain frequencies to play. A Low-Pass (LP) crossover allows only frequencies below its setting to get through which is good in the case of some subwoofers. A High-Pass(HP) filter allows frequencies above its setting to pass through, this is normally used on speakers.
When a crossover is set to FULL it means no filtering is added and the full frequency spectrum is allowed through the amplifier. Filtering is important because feeding a speaker frequencies it cannot reproduce effectively creates distortion.