What does Romans 11:17 mean?

This verse begins an if/then statement that will be concluded in the following verse. Paul is building on the previous verse in which he compared Israel to a tree. In this analogy, he uses versions of the Greek term rhiza, which suggests the life-sustaining part of the plant from the soil surface on down. If the root of the tree is holy, then the branches of the tree will be holy. Paul was making the point that Israel will eventually return to their first nature as the set-apart people of God by coming to faith in Christ.

Now Paul begins a sentence meant for Gentile Christians. He writes that some of the branches of Israel's tree have been broken off. In this context, that seems to mean they have been deliberately pruned away because of their refusal to trust in Christ for salvation. He describes Gentile Christians as being grafted in among the other branches on this metaphorical tree. The Gentiles now receive nourishment through those holy roots, just as believing Jewish people do.

Paul is describing an apparently common practice of olive tree farming. To mingle plants, caretakers can transplant branches from one tree to another. Paul's take on the practice seems unusual, however. It was unlikely that a farmer would graft a wild olive branch onto a cultivated olive tree. However, that may well be Paul's point. God's choice to graft the "wild" and unspiritual Gentile people onto the tree of God's grace to the Israelites also seems unlikely. And yet, this is exactly what God has done.

Paul's if/then statement concludes in the following verse with the "then" part in which he warns Gentile Christians not to be arrogant.