What does John 10:13 mean?

Shepherding was hard (Genesis 31:38–40) and dangerous (1 Samuel 17:34–37) in the ancient middle east. Jesus is comparing His role as a "good shepherd" to false religious leaders (Ezekiel 34). At worst, they are like thieves and robbers who actively prey on the flock (John 10:10). Others are like hired hands who aren't invested in the sheep. They provide a certain level of care—in this case, spiritual leadership—but run away when faced with personal loss or risk (John 10:12). These hired hands don't care for the sheep for the sheep's sake. They only care for what the sheep can do for them. Jesus, by contrast, is willing to lay down His life for the sake of "His" sheep.

This follows from the prior two analogies which Jesus taught His religious critics. The first pointed out that sheep in that time were highly attuned to the voice of their own shepherd (John 10:1–6). Those who rejected Jesus did so for the same reason sheep ignore the voice of a stranger: they're not part of "His" flock. This meant those who reject Jesus were ultimately owned by Satan (John 8:42–47).

The second analogy (John 10:7–9) pointed out that Jesus is the one and only means by which people find spiritual truth. He is "the door," like the single narrow gap in the ancient sheep pen. All people—like all sheep—were either "in" or "out" of this door, and only those "in Christ" are saved.