The neutral zone is the middle area of the ice rink that lies between the two blue lines. This is coined the "neutral zone" because it's the only section of ice that does not belong to either team. Once a player crosses the blue line with the puck into his offensive zone, he is said to be "in the zone", which refers to being in the zone of the other team or in the scoring zone.
The two blue lines on the ice divide the ice into three zones; the offensive, defensive and neutral zones. The zone in which your team's goaltender is located is your defensive zone, since you defend your own goal. The zone where the opposing team's goaltender is located is the offensive zone, since that's the goal you're attacking. The zone in the middle is the neutral zone, since you may be defending or playing offense in this zone.