Jesus being “a little lower than angels” refers to His humanity, not divinity. As God, He is superior to everything in creation, including angels (see, for example, Hebrews 1). However, when He took on human form (Philippians 2:6–7), for a time He was placed under the angels. This is because all humans were created to rule creation under God (and the angels—Psalm 8:5). However, as Hebrew 2:7 attests, He was made lower than the angels only “for a little while.”
Jesus was sent to live perfectly and die for sinful mankind. After He did, the Father “highly exalted Him” (Philippians 2:9) to His right hand (Hebrews 1:2), giving Him authority over the angels (Hebrews 1:3), something humanity has not yet received (see, 1 Corinthians 6:3) because of our rebellion and sin nature. Therefore, Jesus was “a little lower than angels” only in His humanity and only for the 30-some years that He lived on earth. After He completed His mission and ascended to heaven, He was elevated above them.
We were given authority over creation that was just a little lower than God’s authority (Genesis 1:26). When Adam sinned, creation was corrupted, as well as all of Adam’s descendants (Romans 5:12). Since then, we have neither ruled creation nor obeyed our Creator rightly.
In order to save us, God sent His Son (John 3:16). Being fully God (John 1:1), Jesus is incapable of sinning (Hebrews 4:15). However, being fully human (Philippians 2:6–7), He is like us (Hebrews 2:17). That means that Jesus had the same responsibilities before God that we have, including obedience and rule over creation.
Jesus lived perfectly on this earth. Because only humans die, Jesus was able (and willing) to die as a substitution for sinful men and women. Three days later He rose again (1 Corinthians 15:3–4), proving He was God, and is now sitting at the right hand of the Father (Hebrews 1:3). Because of Jesus’ death, we have a way of escape from the wrath due our rebellion. Also, because of His perfect obedience, the Father raised Jesus in His humanity to be above all creation, even the angels. Jesus, then, is the perfect human and perfect fulfilment of what God created man to do and be like.
In light of Jesus’ authority, there are two things we must do. First, as the only perfect human sacrifice, Jesus is also the only way to be saved (John 14:6). We must repent of our sin and trust in Him and His work for our salvation. Second, as the ruler who is sitting at the Father’s right hand, He also has all authority (Matthew 28:18). This means that we are to live for Him, obeying Him and giving Him all glory and honor as the King of Kings (Revelation 19:16).