The passage referred to is (Isa 6:8-10) and is quoted in all of the other gospels and by Paul in Acts (Mat 13:14-15,  Mark 4:12,  Luke 8:10, Acts 28:26-27). In the synoptic gospels it is used to show that people who are unbelieving hear the words spoken, but cannot discern their meaning. Paul uses it to show why salvation was given to the Gentiles.

Isaiah 6:8-10  Then I heard the voice of the Lord saying, “Whom shall I send? And who will go for us?” And I said, “Here am I. Send me!”  He said, “Go and tell this people: “‘Be ever hearing, but never understanding; be ever seeing, but never perceiving.’  Make the heart of this people calloused; make their ears dull and close their eyes. Otherwise they might see with their eyes, hear with their ears, understand with their hearts, and turn and be healed.”

Matthew 13:14-15  In them is fulfilled the prophecy of Isaiah: “‘You will be ever hearing but never understanding; you will be ever seeing but never perceiving.  For this people’s heart has become calloused; they hardly hear with their ears, and they have closed their eyes. Otherwise they might see with their eyes, hear with their ears, understand with their hearts and turn, and I would heal them.’

Mark 4:12  so that, “‘they may be ever seeing but never perceiving, and ever hearing but never understanding; otherwise they might turn and be forgiven!’”

Luke 8:10  He said, “The knowledge of the secrets of the kingdom of God has been given to you, but to others I speak in parables, so that, “‘though seeing, they may not see; though hearing, they may not understand.’

Acts 28:26-27  “‘Go to this people and say, “You will be ever hearing but never understanding; you will be ever seeing but never perceiving.”  For this people’s heart has become calloused; they hardly hear with their ears, and they have closed their eyes. Otherwise they might see with their eyes, hear with their ears, understand with their hearts and turn, and I would heal them.’

“deadened” (NIV) = “hardened” (KJV) = “hardened and benumbed”  (Amplified) The Greek word is poroo which means “to cover by forming a callous,” a very descriptive word indeed.

To see with the eyes is descriptive of discerning spiritual truths; to understand with the heart means to consent to those spiritual truths and accept and apply them; and to turn refers to turning away from sin, the flesh, and the world and turning toward God and His desires for you. It is when you turn that God heals you, which means that he forgives and cleanses you of your sin and makes you righteous.

Augustine notes that, “God thus blinds and hardens, simply by letting alone and withdrawing His aid”.

Everything is ascribed to the hand of God. His purposes are not thwarted, even by the opposition of evil men, or, as Barclay puts it, “… even man’s unbelief can be used to further God’s eternal purposes.”