What does Luke 18:10 mean?

This begins the parable of the Pharisee and the tax collector. From here through the end of the chapter, Jesus contrasts different reactions to the kingdom of God to show that humility is an essential ingredient of faith.

In Jesus' era, the Pharisees are a particular Jewish sect. They are unofficial religious leaders in Jewish culture. Their realm is among the people and in the synagogue; they do not have authority in the temple like the priests do and very few are in the Sanhedrin—the Jewish ruling council—which is typically filled with Sadducees. Like Sadducees, Pharisees strongly believe in the Pentateuch: the five books of the Mosaic law. Unlike Sadducees, they believe in the resurrection of the dead. They are most identified by their adherence to extra-biblical rules that were developed to put a hedge around the Mosaic law. Like the Zealots, they want the Romans gone and the Jews to rule their own nation again. But they are afraid of exile, so they try to appease both God and the Romans.

While Jews tend to hold Pharisees in high regard, they despise tax collectors. In Jewish areas, tax collectors are Jews who work for Gentiles who have taken a contract to collect money from the people for the Roman government. The man who holds the contract adds his own fee to what the Romans demand, and the tax collector, himself, is welcome to collect even more for himself. Piling these commissions on top of the tax make it difficult for people who barely survive on what they have left. In addition, the close contact tax collectors have with Gentiles leaves them ceremonially unclean. The fact that this tax collector is at the temple means he must have ceremonially purified himself. His presence there cost him something.

The King James Version uses the term "publican": someone who deals with public revenue. Technically, these publicans are the Gentiles who hold the contract, not the tax collectors who collect the money for the publicans.