What does Matthew 12:18 mean?

Matthew is referencing Isaiah 42 and applying it to Jesus. That passage might have initially seemed to refer to Israel, but Matthew's version of the passage fits Jesus perfectly. Jesus is sometimes described as the ultimate expression of Israel. In that way, He fulfills Isaiah's prophecy in these verses.

The passage begins with phrases that sound very much like what the voice of God the Father said from heaven about Jesus immediately following His baptism by John the Baptist, "This is my beloved Son, with whom I am well pleased" (Matthew 3:17). It is similar, as well, to the Father's words about Jesus later in Matthew during what it known as the transfiguration (Matthew 17:5).

About 700 years or so before those moments, Isaiah quotes God as saying, "Behold, my servant whom I uphold, my chosen in whom my soul delights." The word translated as "servant" in Isaiah can also be read as "son." Jesus fits both, of course, in relation to God the Father. Matthew seems to be using the Septuagint: a Greek translation of the Hebrew Scriptures.

The second part of this verse also fits with that moment following Jesus' baptism, which involved "the Spirit of God descending like a dove and coming to rest on him" (Matthew 3:16). Isaiah quotes God as saying, "I will put my Spirit upon him."

Isaiah next turns to the work this servant will do in proclaiming justice to the nations—in this context, meaning the Gentiles. Jesus came first to proclaim the good news to His people Israel, but soon His followers will take the message of Jesus to all the people of the world.