vtctl is a command-line tool used to administer a Vitess cluster. It allows a human or application to easily interact with a Vitess implementation. Using vtctl, you can identify master and replica databases, create tables, initiate failovers, perform sharding (and resharding) operations, and so forth.
As vtctl performs operations, it updates the lockserver as needed. Other Vitess servers observe those changes and react accordingly. For example, if you use vtctl to fail over to a new master database, vtgate sees the change and directs future write operations to the new master.