“Now” (NIV) or “for” (KJV) links this verse with the preceding one.  Jesus had to go into Galilee to show that this was indeed true.  Loyd states that “He had to go on and get on with the business of being rejected by the many and accepted by only the few.” (qt’d in Morris p. 285)

Some argue that “his own country” (patris) refers to Judea although John 4:1-3 refutes this by showing that His ministry was quite successful in Judea.  Others argue that patris refers to Nazareth which is how this proverb is applied in the synoptic gospels, but John shows no indication of using it to apply to Nazareth.  The probable meaning is Galilee since John is speaking of the motive of Jesus in going into Galilee where He has no fame as He now does in Judea and Samaria.

John 4:1-3  The Pharisees heard that Jesus was gaining and baptising more disciples than John,  although in fact it was not Jesus who baptised, but his disciples.  When the Lord learned of this, he left Judea and went back once more to Galilee.