Jesus is both the Son of God, and the son of Mary. As Jesus was the Son of God, the Devil and his followers had to submit to Him and not dare to 'tempt' Him. Devils once lamented 'Have you come to destroy us?' Lk 4,34. The Devil tempted Jesus as the son of Mary only, not as the Son of God. Jesus was led by the Spirit to indicate that as the son of Mary, the Spirit of God led him into the wilderness. Each temptation the Devil began with the statement 'if you are the Son of God' which means the Devil challenged Jesus' identity.
After a long forty days fasting, Jesus felt hungry, and the Devil tempted Jesus three times. The first temptation was about self indulgence. The second temptation was about the accumulation of power, and the third temptation was about pride. In his public ministry Jesus didn't change stone into a loaf, but he actually fed the crowd with two fish and five loaves Lk 9,10ff. The second temptation was about the expectation of the people, that he would become their king to liberate them from the power of the Roman Empire. This is in contrast to Jesus' mission, he proclaimed in the Gospel of Luke 4,18-19. His mission is mainly about saving others from the power of darkness, not much about worldly power. The third temptation was about pride. Instead of jumping off from the parapet of the Temple, Jesus chose to be hung on the cross to draw people to himself. In one of the penitential rites, we confess that: Lord Jesus, you were lifted up to draw all people to yourself. And the next verse: you shouldered the cross, to bear our suffering and sinfulness.
Both Jesus and the Devil quoted from the Old Testament but there is a huge difference. The Devil used the Sacred Text to show off his knowledge of the Sacred Text, but had no love for it. For Jesus, on the other hand, the Sacred Text was very much close to his heart. Today many quote the Sacred Text to make their point, and we hope and pray, they believe and love what they quote.
The temptations of Jesus give us several lessons to learn from. First, we don't fight against temptations with our own strength and knowledge, but we rely on the strength of God's Word and grace to combat temptations. Second, a temptation is not yet a sin. It is a sin when one commits oneself to take part in carrying out the temptation. Refusing to listen to his voice, we make the Devil powerless to compel us to follow his will. Third, God's Spirit was with Jesus, and Jesus listened to his voice. The same Spirit is also with us, and we pray for the wisdom to listen to the voice of the Spirit. Refusing to listen to his voice means we rely on our own strength and power and that leaves a door wide open for the Devil to come in. Finally, the Devil was exhausted and went away but he promised to return at other times. The Devil was hungry with temptations while Jesus was hungry to save us from damnation.