What does John 7:5 mean?

Of all the people in the world who should have accepted Jesus as Messiah, his immediate family are be at the top of the list. After all, nobody knew Him as well or saw His character as clearly. And yet, this same familiarity seems to produce the opposite effect. Jesus' own brothers—other biological children of Mary—don't yet accept His ministry or His mission. Part of this is cultural: Jewish tradition suggested that the Messiah would be relatively unknown prior to His emergence (John 7:27).

This is also proof of several ideas explored in the gospel of John. Later in this chapter, Jesus will point out that obedience must come before knowledge, otherwise people will not believe (John 7:17). A year earlier, after healing a man at the Pool of Bethesda, Jesus pointed out that the men rejecting Him were well-educated in the Scriptures, but refused to believe (John 5:39–40). Seeing miracles won't convince those who aren't looking for spiritual truth (Luke 16:31). Judas Iscariot is the prime example of someone who was presented with as much "proof" as could possibly be offered, yet still rejected Christ.

On a more positive note, tradition suggests that at least two of Jesus' siblings became believers after His resurrection. These include both the author of the New Testament book of James, and the author of the book of Jude.