Jesus came to earth as the second Adam, to stand as a man where Adam fell.
The first man is of the earth, earthy: the second man is the Lord from heaven (1 Corinthians 15:47, KJV)
Though He was also fully God, He did not use His Godly nature to withstand Satan's temptations. Instead, He took on the flesh of a sinless man, and defeated Satan where Adam failed.
But we see Jesus, who was made a little lower than the angels for the suffering of death (Hebrews 2:9)
For if through the offence of one many be dead, much more the grace of God, and the gift by grace, which is by one man, Jesus Christ, hath abounded to many. (Roman 5:15)
Who, being in the form of God, thought it not robbery to be equal with God: But made himself of no reputation, and took upon him the form of a servant, and was made in the likeness of man" (Philippians 2:6-7, KJV)
Thus, when read in the context of these passages, Jesus, God the Son, humbled Himself in the form of a man, and defeated Satan in obedience to God, without using His divine nature.
In the weakness of human flesh, the possibility of falling into sin was a reality. In the Garden of Gethsemane, Jesus struggled and prayed "not as I will, but as you will" (Matthew 26:39). Being sinless, temptation came to Jesus externally, while for us who are fallen, temptation comes from within - the sinful inclinations of our hearts are brought to surface by Satan and his demons.
Jesus trusted in the Father's power. It was a life of faith - faith in God's love and provisions - that Jesus rested in, and lived a perfect life. This life of righteousness lived as man He now gives to us, all who lives in Him by faith.
With so much at stake for the salvation of men, it is perhaps one of the strongest argument for the Trinity - it is God Himself who came for men's redemption. It was also God's self-denying love that laid down His own life at the cross for the world. And until the cross, no created being understood the character of God in as much clarity as now. The very relationship among members of the Trinity, a love that "seeketh not her own" has its source in the heart of God, is expressed perfectly in the interactions between Jesus and God the Father.
The second part of your question, "Therefore, God elevated him to the place of highest honor" relates to the fact that by taking on the form of a man, Jesus "made Himself of no reputation" (Philippians 2:7) and "lower than angels" (Hebrews 2:9) to gain victory at the cross. As a man, He brought honor and glory to God, thus God elevated Him to the place of highest honor and gave Him the name above all other names, even though it is really no greater a title than His original position.