A NPN transistor conducts when-
The voltage between the base and emitter is positive at the base and negative at the emitter because for an NPN transistor, the base terminal is always positive with respect to the emitter i.e., an emitter is always negative w.r.t. the base. Also, the collector supply voltage is positive with respect to the emitter. So for a bipolar NPN transistor to conduct the collector is always positive with respect to both the base and the emitter.