The name Jesus means "Savior." It is the same name as Joshua in the Old Testament. It is given to our Lord because "He saves His people from their sins." This is His special role. He saves them from the guilt of sin, by cleansing them in His own atoning blood. He saves them from the dominion of sin by putting in their hearts the sanctifying Spirit. He saves them from the presence of sin, when He takes them out of this world to rest with Him. He will save them from all the consequences of sin, when He shall give them a glorious body at the last day.
Jesus is a very encouraging name to weighted-down sinners. He, who is the King of kings and the Lord of lords, might lawfully have taken some more high-sounding title. But He does not do so. The rulers of this world have often called themselves great, conquerors, bold, magnificent, and the like. The Son of God is content to call Himself Savior. Those seeking salvation may draw near to the Father with boldness, and have access with confidence through Christ. It is His role and His delight to show mercy. "For God didn't send his Son into the world to judge the world, but that the world should be saved through him" (John 3:17).
Jesus is a name, which is especially sweet and precious to believers. It has often done them good. It has given them what money cannot buy - that is, inward peace. It has eased their wearied consciences and given rest to their heavy hearts. The Song of Solomon describes the experience of many, when it says, "Your name is oil poured forth" (Song of Solomon 1:3). Happy is the person who trusts not merely in vague notions of God's mercy and goodness, but in "Jesus."
Adapted from The Gospel of Matthew by J.C. Ryle (Chapter 1).