What does Luke 18:6 mean?

Jesus begins to tell the moral of His parable. A widow comes to a judge for justice. This seems to mean that she demands her right to present a case in court, and that she wants her adversary to follow the law, as well. The judge is not necessarily corrupt, but he's completely amoral. He doesn't care about God, people, or the Mosaic law. He is not motivated by duty, shame, or any sense of justice. He dismisses the widow without a thought (Luke 18:1–3). Perhaps her case seems trivial, or he doesn't want the bother of going through a long process.

The widow is not finished. She comes to him "continually" and "keeps bothering" the judge. She's so relentless that the judge feels she will "beat [him] down" (Luke 18:5). So the judge relents and settles her case (Luke 18:4–5). He doesn't act out of love, mercy, truth, or any other positive impulse. He's benefitting himself by removing an irritation.

Jesus tells His disciples to listen to what the judge says. As unrighteous as he is, he will give justice if the alternative costs him enough. Jesus goes on to contrast this judge with Father God. He is the God of justice. Justice is one of the foundational truths of His creation. The widow must beg a human judge for justice, but God will give it freely to His elect. They just need faith. The question is, when the time is ripe for Jesus to return and judge the evil of the world, "will he find faith on earth?" (Luke 18:7–8).