Answer: Jesus teaches us that those people who find the righteousness that they "hunger and thirst" for, and are then persecuted because of that righteousness, are blessed, because the kingdom of heaven is theirs, (verse 6 and 10).
MORE INFORMATION AND/OR OTHER SCRIPTURE REFERENCES:
Matthew 24:9: [Jesus said,] "Then you will be handed over to be persecuted and put to death, and you will be hated by all nations because of Me."
John 15:20: [Jesus said,] "Remember the Words I spoke to you: ‘No servant is greater than his master.' If they persecuted Me, they will persecute you also."
2 Timothy 3:12-13: "In fact, everyone who wants to live a godly life in Christ Jesus will be persecuted, while evil men and impostors will go from bad to worse, deceiving and being deceived."