to sum up: to gather many separate things under one comprehensive whole
This is a learned, almost technical word that Greek orators used at the close of a speech, when they pulled all their scattered points together into one brief summary. It does not come from the word for a person's head (κεφαλή); it comes from a related word (κεφάλαιος) meaning the main point, the heading at the top of a column, or the total at the bottom of a ledger. So at its core the verb means to bring a whole range of things together and account for them as one comprehensive sum.
Paul uses it just twice, and the two uses sit at very different scales. In Romans he uses it of teaching: the many separate commandments are all summed up, gathered without remainder, under the single command to love your neighbor. In Ephesians he stretches the same idea to the whole created order: God's plan is to bring everything in heaven and on earth together into one in Christ. The smaller, everyday sense and the vast cosmic sense are the same action seen at two sizes, which is why they belong to one meaning rather than two.
The Ephesians use is one of the most debated words in Paul's letters, and the debate is worth flagging plainly. Because the word sounds close to the ordinary Greek word for head, and because Paul calls Christ the head over all things just a few lines later, many readers hear an echo of headship in it, as if it meant to bring everything under one head. Most careful study concludes that the plain sense is still to sum up or unite, with the head idea present at most as a faint overtone carried by the surrounding verses, not by the word itself.
Nuances
Disputed
In Ephesians 1:10, whether the verb carries only its established lexical sense "to sum up / bring into unity", or also a deliberate wordplay on the word for "head" yielding "to head up all things in Christ".
- majorityThe verb means "sum up / bring into one comprehensive unity"; the head idea is at most a faint contextual echo from Christ being called the head a few verses later, not part of the word's own meaning.; Andrew T. Lincoln, Ephesians (WBC 42, 1990), pp. 32-33; Ernest Best, Ephesians (ICC, 1998), pp. 140-143; J. B. Lightfoot, Notes on the Epistles of St Paul
- minorityThe surrounding head-Christology makes the resonance with "head" theologically operative, so the verb should be rendered with headship in view, as "head up" or "comprehend under one head, the Messiah".; H. Schlier, TDNT 3:673-682; Markus Barth, Ephesians 1-3 (AB 34, 1974), pp. 89-92
- contestedA mediating reading combines both: "to unite under one head", holding the lexical "sum up" together with a contextually audible head-resonance.; Harold W. Hoehner, Ephesians: An Exegetical Commentary (2002), pp. 216-220; Clinton E. Arnold, Ephesians (ZECNT, 2010), pp. 89-90