something that has been made: a product or piece of work, and in Paul above all the handiwork of God the maker
Greek builds this noun from the everyday verb meaning "to make" or "to do," and its ending marks the result of that action: the thing produced, not the act of producing it. So the plain sense is a made thing, a product, a piece of work. Everyday Greek could use it for a crafted metal object or, in literary writing, for a poem, but that literary sense is not what the Bible reaches for.
In the Greek Old Testament the word was used over and over for God's works and for the things people make, regularly translating a common Hebrew word for "work" or "deed" (מעשׂה). Paul inherits that usage, and both times he uses the word it means the product of God's making.
In Romans it is the visible creation, the made world that shows its maker so plainly that no one has an excuse for ignoring him. In Ephesians it is God's people, those he has made new in Christ. Paul reached for this word over the nearby κτίσις, "creation," in the same Romans sentence precisely to spotlight the tie between a maker and what he makes: God is the one who works, and the world (and his people) are his handiwork.
Ephesians also sets up a deliberate contrast. Salvation is not earned by our own ἔργον, our works, and yet we are made by God for good works. We are the product; the good deeds are the purpose, not the price.