What does John 9:31 mean?

A general theme of the Old Testament is that God's attention is tuned to the prayers of those who follow Him, and generally against the prayers of those who oppose Him. While not an absolute rule, this principle takes on a greater meaning when applied to miracles. Elijah used prayer, and God's miraculous response, as proof that his preaching was the truth (1 Kings 18:20–40). Jesus' supernatural works are meant to be "signs" that He is operating with divine power, and godly approval (John 12:37–38; Isaiah 29:18; 35:5; 42:7). For the scribes and Pharisees to dismiss Jesus' obvious power by calling Him a "sinner" (John 9:16) is proof that they're grasping at straws.

This specific point is being made by a man who was born blind, but healed by Jesus (John 9:1–7). Jesus' religious critics have responded to this man's testimony with insults and anger (John 9:28, 34), demonstrating that they have no reasonable arguments to use. As part of this rejection, the scribes and Pharisees claimed to be followers of Moses, but that they did not know who Jesus was or where He was from (John 9:29). The beggar is pointing out that even if they don't know everything about Jesus, the fact that He's performing healing miracles is evidence enough.

In the next verses, this man will continue to apply this theme by pointing out that Jesus' miracle is not only a potent sign—it's a unique sign which no other prophet had accomplished before.