Zone Starts, or rather Offensive Zone Start %, measures the percentage of time when a player starts in the offensive zone. A Zone Start ignores starts in the neutral zone, and begins when a player starts his shift in a zone (beginning with a faceoff).
Zone Starts are a great stat to utilize when, for example, determining how a coach views a certain player, from a practical standpoint when a new player is acquired, as well as finding out why a player's Corsi is trending high or low.
A coach has such players start in the offensive zone to keep the puck in the offensive zone, thereby creating better scoring chances, and making sure the opponents' possession is kept to a minimum, which helps the team and the player's Corsi numbers.