Jesus was born to save His people. He did not come into this world to try to save, hope to save, nor might save. Be sure to know that Jesus saves all who come to God through Him. The truth is this, we cannot save ourselves. We need a Savior, and there is only One. His name is Jesus.
"And she shall bring forth a Son, and you shall call His name JESUS, for He will save His people from their sins" (Matthew 1:21).
When the Son of God was born of flesh to dwell among us, the name given Him was Jesus. That name means "Jehovah is salvation." Jehovah is the covenant name for God. The name tells the story, Jehovah God saves people through His Son.
When we read Jesus will save His people, that is certainly not talking about Jews only. Jesus was born a Jew, but Jesus saves people from every race and nation. He draws people from all nations to Himself (John 12:32). Jesus saves all who repent and come to Him by faith. He is calling people out of all nations (Revelation 5:9).
Jesus saves His people who believe the gospel. And, what is the gospel? It is clearly defined in 1 Corinthians 15:3-4, "that Christ died for our sins according to the Scriptures, and that He was buried, and that He rose again the third day according to the Scriptures."