Unless otherwise indicated, all Scripture quotations are taken from the NASB (1995 edition).
The Greek in the title says it all: "For the gifts [τά χαρίσματα] and calling [κλῆσις] of God are irrevocable [ἀμεταμέλητα]" (Romans 11:29).
In context, what is this verse talking about? Is it talking about the spiritual gifts of the church? Why not? It has χαρίσματα (charismata, meaning "gifts"), so it must be talking about that, right? Surely, it must.
Nope, it isn't. This verse is not talking about the church (by church I mean Christians). Romans 9–11 is talking about Israel---specifically, the majority of Israel, which at Paul's time and in our own day today did not and still does not believe Jesus to be the Messiah who came to save the world and rescue us from our sin. So what does that mean for Romans 11:29, quoted in the title? It means that God's gifts to Israel and His calling of Israel (described in Romans 9:1-5) are ἀμεταμέλητα (ametameleta, meaning "irrevocable"). They can't be undone.
Interestingly, the book of Romans is often reduced in evangelical circles to a book of doctrine, and if any part of Romans 9–11 is mentioned at all, it's usually Romans 10:9-10 (the "Roman road" to salvation). Somehow, the fact that this is a letter written by a first-century Jew to a Jewish and Gentile church escapes us. We sometimes acknowledge this, but in practice we often forget it, treating the text as if Paul just sat down one day and decided, "I'm going to write a theological essay today that will be considered Scripture, and it will include all my thoughts on God, Jesus, and salvation." Romans becomes a string of prooftexts about how we're saved, and although Romans certainly does talk about salvation from God's wrath through Jesus (see Romans 3–5, for example), any exegete of the book knows that this does not exhaust what Paul wanted to say to this church in Rome.
For Paul, this was a letter---one inspired by God, to be sure, but I doubt Paul was thinking, "This letter I'm writing is going to be part of Scripture." A major theme of this letter, which is not just discussed in Romans 9–11, is the story of Israel and the inclusion of Gentiles in God's family. Notice, for instance, the famous passage of Romans 3:28: "For we maintain that a man is justified by faith apart from works of the Law." Most people isolate this passage and present it as one of their many prooftexts. But they forget the next verse: "Or is God the God of Jews only? Is He not the God of Gentiles also? Yes, of Gentiles also" (Romans 3:29). What is the point Paul was trying to get across here? It appears that verses 28 and 29 are linked and NOT separate thoughts altogether.
Sidebar: If you're familiar with the current justification debate between John Piper and N.T. Wright, you know that seeing this letter in its first-century Jewish context is a major part of this discussion (did first-century Judaism tend to be legalistic, or did it teach grace?). If you have no idea what I'm talking about, the Christianity Today articles here and here do a good job of summarizing what all this is about. Also, if you're interested in this important discussion, here are two books I'd recommend:
1. John Piper, The Future of Justification: A Response to N.T. Wright (Wheaton, IL: Crossway Books, 2007). Piper's passion for God's grace in this book is compelling. I disagree with his views on first-century Judaism and Paul (see pages 133-158), but I couldn't agree more with his enthusiastic commitment to preaching God's grace as revealed through the death and resurrection of Jesus the Messiah.
2. N.T. Wright, Justification: God's Plan and Paul's Vision (Downers Grove, IL: InterVarsity Press, 2009). N.T. Wright brought the split between Romans 3:28 and 3:29 to my attention, and his comments on how the history of the Western church might have been different if they had read Paul in light of his Jewish soteriology are also insightful: "[There would have been no] split between Romans 3:28 and Romans 3:29. No marginalization of Romans 9–11. No scrunching of the subtle and important arguments about Jew-plus-Gentile unity in Galatians 3 onto the Procrustean bed of an abstract antithesis between faith and works." Of course, N.T. Wright hasn't convinced me of his overall thesis (I'm still thinking it through), but I appreciate his sensitivity to (A) Scriptural authority in spite of all tradition and (B) the first-century Jewish context of Paul's letters.
Of course, Romans is not the only book reduced to a systematic theology textbook, with the Jew-and-Gentile-now-one-in-Christ theme shoved to the corner. Ephesians is often mined strictly for its "saved by grace through faith" passage in Ephesians 2:8-9, with not much regard for verse 10, and perhaps less regard for verses 11-22, which stress that the wall of partition between Jew and Gentile is now torn down in Messiah Jesus.
Paul did teach that we're saved by grace, and that is incredibly important. But he also taught about Jews and Gentiles coming together as one in Messiah Jesus, which is also incredibly important. That means that everyone can be "in Messiah" (or "in Christ"), not just the Jews.
Also important to emphasize is that Paul was deeply concerned for his fellow Jews who still did not believe in Jesus. That's where Romans 11:29 comes back into the discussion. God's gifts and calling of the Jewish people are irrevocable. Let me end with Paul speaking for himself in Romans 11:28-32 concerning his fellow Jews who did not believe Jesus to be the Messiah (see all of Romans 9–11 here):
From the standpoint of the gospel they are enemies for your sake, but from the standpoint of God's choice they are beloved for the sake of the fathers; for the gifts and the calling of God are irrevocable. For just as you [Gentiles] once were disobedient to God, but now have been shown mercy because of their disobedience, so these also now have been disobedient, that because of the mercy shown to you they also may now be shown mercy. For God has shut up all in disobedience so that He may show mercy to all.