What does the Bible mean when it says all things are under Christ's feet?

Scripture means God has placed all things under Christ’s sovereign authority and made Him head over all things for the Church, His Body. The Church is His complement and completing, so what Christ possesses, believers will one day share by faith, because the Book says it.

In Ephesians 2, Les teaches that even the Lord Jesus, the crowning Creator and God of the Universe, loves His blood-bought Church, His Body, and does not consider Himself complete until He has us in His presence. God has put all things under Christ’s feet and gave Him to be head over all things to the Church, which is His Body, the complement or completing of Him who fills all in all. Les says this is why what He has, we’re going to one day have, and we know it by faith because the Book says it. He adds that he doesn’t know any other way to explain it; the Book says so, and on that basis we believe.

Ephesians 1:22

And hath put all things under his feet, and gave him to be the head over all things to the church,

See the rest

What does it mean that Christ is head over all things for the Church?

Christ's headship over all things means God has placed everything under His feet and appointed Him head over all things for the Church, His Body. The Church is His complement, completing Him who fills all in all, and He will not consider Himself complete until believers are in His presence.