Nuclear recoil events produced by neutron scatters form one of the most important classes of background in WIMP direct detection experiments, as they may produce nuclear recoils that look exactly like WIMP interactions. In DarkSide-50, we both actively suppress and measure the rate of neutron-induced background events using our neutron veto, composed of a boron-loaded liquid scintillator detector within a water Cherenkov detector. This paper is devoted to the description of the neutron veto system of DarkSide-50, including the detector structure, the fundamentals of event reconstruction and data analysis, and basic performance parameters. Show Partial Abstract