'For he must reign, until he has put all his enemies under his feet.'
For Christ having taken His throne after His resurrection, has continued His reign, and must go on reigning until the final defeat of all His enemies both in Heaven and earth. And once they are under His feet as a result of His second coming, when all rule and authority and power has been abolished, then He will hand the crown to His Father.
'Rule and authority and power' indicates all that is in rebellion against God, all who have chosen to be independent of Him and establish themselves over against Him, whether Satan, his minions in the heavens, or his dupes on earth. All are to be 'put under His feet'. This idea, related to Kingship, comes from Psalms 110:1 compare Matthew 22:44, revealing Jesus Christ as the greater David, God's Anointed, and Philippians 2:10 as taken from Isaiah 45:23.