“[S]aving grace . . . is God’s giving us a sovereign joy in God that triumphs over all other joys and therefore sways the will. The will is free to move toward whatever it delights in most fully. But it is not within the power of our will to determine what that sovereign joy will be.” 
Some Background Info
Before I dive right into this topic, perhaps some background would be helpful. The quote above comes from John Piper’s book God’s Passion for His Glory: Living the Vision of Jonathan Edwards. In the first part of the book, Piper gives a brief biography of Edwards; included in this section is Piper’s own personal story of how he encountered Edwards’s writings and the impact they have had on his life and ministry. The quote comes from the section in which Piper talks about his experience of reading Edwards’s book The Freedom of the Will. This book is Edwards’s most influential philosophical treatise ever written. In context, the quote above comes from Piper summarizing Edwards’s own view of free will. Speaking personally, I have enjoyed the first part of this book so much that this was my second time reading through it.
Explaining the Quote
I mentioned a few days ago on Facebook that I hoped to offer some thoughts on this quote from Piper. As I’ve reflected on how to begin, I think the best place to start is with the latter part of the quote and then work my way back to the beginning of the sentence. With that said, here goes nothing: In the second and third sentences Piper writes, “The will is free to move toward whatever it delights in most fully. But it is not within the power of our will to determine what that sovereign joy will be.”
In these two sentences Piper highlights the fact that both before and after our conversion, we will always choose those things which we believe will bring us the greatest amount of joy. Thus, as he says, our “will is free to move toward whatever it delights in most fully.” However, prior to our conversion we have no desire to choose God or to choose those things which please God. Left to ourselves, then, we willingly choose to sin. Given this picture, it’s no wonder the Bible describes unbelievers as “slaves to sin” (Jn. 8:34; Rom. 6:15-17, 20; cf. Eph. 2:1-3). For this reason, Piper’s next sentence makes complete sense: “. . . it is not within the power of our will to determine what that sovereign joy will be.” In other words, the sovereign joy of an unbeliever is sin. They do not have the ability to stop loving sin. They sin both willingly and joyfully. Sure, there may be times when they feel guilty for some things they do, but that’s expected since they are made in God’s image. That being said, they do not have the power to stop loving sin and to start loving God. This requires “saving grace,” to use Piper’s words.
Two Beautiful Words
Saving grace. Those are two beautiful words. Some theologians call it sovereign grace, but all theologians call it “regeneration.” That is what we need. And that’s what Piper is insisting has the power to “sway the will.” This is because when God grants us new life (i.e., he “regenerates” us), he makes us a completely new person (2 Cor. 5:17). He changes our desires, affections, priorities, etc. If this seems a bit exaggerated, just read Jesus’ parables in Matthew 13:44-46. The way the Bible describes conversion doesn’t make it seem like a person can be half-hearted in his or her obedience to, and love for, Christ. All of this leads us to the conclusion that when God intervenes in a person’s life, he grants them a faith in him that includes a joy in him that “triumphs over all other joys.” This is the work of regeneration. And as R. C. Sproul writes, “In regeneration, God plants a desire for Himself in the human heart that otherwise would not be there.” Desire is an all-important word as well. Before our conversion we had no desire for God either. Only after God gives us new life do we have a desire to trust him, love him, and serve him. Only after God gives us new life do we have a “taste” for him. I love the way Jonathan Edwards spoke about the effect of regeneration on a person:
The first effect of the power of God in the heart in regeneration, is to give the heart a Divine taste or sense; to cause it to have a relish of the loveliness and sweetness of the supreme excellency of the Divine nature.
I couldn’t say it any better than that. I hope this helps.
 John Piper, God’s Passion for His Glory: Living the Vision of Jonathan Edwards. With the Complete Text of The End for Which God Created the World (Wheaton: Crossway, 1998), 87.
 Since this point has been made by numerous philosophers, no effort will be made to defend it here. See, e.g., Aristotle, Nichomachean Ethics (trans. F. H. Peters; NY: Barnes & Noble, 2004), 1. 1; Blaise Pascal, Pascal’s Pensees (trans. W. F. Trotter; NY: E. P. Dutton, 1958), 113, thought #425.
 R. C. Sproul, Essential Truths of the Christian Faith (Carol Stream: Tyndale, 1992), 172.
 Jonathan Edwards, Treatise on Grace, ed. by Paul Helm (Cambridge: James Clark and Co., 1971), 48-49.