Ephesians 4:10 (ESV)
"He who descended is the one who also ascended far above all the heavens, that he might fill all things."
What does it mean when it says "that He might fill all things"?
Fill with what - his spirit?
The Greek word used here (πληρόω, pléroó) has a range of meaning which includes:
to make full, to fill, to fill up
to render full, i.e. to complete;
properly, to fill up to the top
to perfect, consummate
to carry into effect, bring to realization, realize
This declaration of Paul is that Christ ascended to heaven in order to fill all things, to complete them and render them perfect.
In the context, this is specifically regarding the church. He goes on to explain how Christ will do this:
This would certainly include the filling of the Holy Spirit, which is the way Christ indwells his body on earth. Through the Holy Spirit, Christ will bring his body into maturity, evidenced by unity.
The emphasis in the passage is on the ascension, which is the enthronement of Christ in heaven. From this seat of power he is the head of all, bringing all things in heaven and earth together under one head (Eph 1:10) and uniting the Jews and Gentiles into one body (Eph 2:14; 3:6).