What does John 10:3 mean?

Sheep pens in Jesus' era were constructed with sturdy walls and a single doorway. This allowed easy control over what animals got in or out, and which people could access the sheep. The gatekeeper was not merely minding the opening. There were often no physical barriers across that opening; a gatekeeper was always on duty. To rest, or even to sleep, the gatekeeper would literally lay across the gap. This will be used in Jesus' second metaphor, where He claims to be "the door of the sheep."

The gatekeeper of the pen would ensure that only approved shepherds—those who had claim on a flock inside—could get in or out. Anyone trying to climb over the walls was, by definition, up to no good. Those allowed in by the gatekeeper were legitimately allowed to be there. Multiple flocks would be kept in a single pen. To get his flock out, all that shepherd had to do was call. The sheep, having been raised and cared for by that single person, would respond. Members of other flocks would not come in response to that voice.

Jesus is using this analogy in response to the religious leaders of Jerusalem. They obstinately refuse to recognize His miracles and His message. In plain terms, these men don't listen to His voice because they are not "His" flock. They are, as Jesus pointed out in other discussions, subjects of Satan (John 8:42–47).