“So then it is not of him who wills, nor of him who runs, but of God who shows mercy.”

It:

Refers to how people are given God’s salvation, in answer to the question Paul was looking at, of why some people are saved and others are not, or of how God chooses whom to give salvation.

Him who wills:

Refers to a person choosing or desiring salvation (an inner activity). This means that the reason God gives salvation to someone does not depend on the the strength of their desire for it.
But this seems contrary to Jesus statement in the Beatitudes, in Matthew 5:6, “ Blessed are those who hunger and thirst for righteousness, For they shall be filled.”

Him who runs:

Refers to human effort or works. Trying to win salvation by our own effort in the race of life has no effect (our external activity).
But this seems to contrast with verses where Paul uses this image of running the race in a positive way:
1 Corinthians 9:24, “… those who run in a race all run, but one receives the prize? Run in such a way that you may obtain it.”
And 2 Timothy 4:7, “I have fought the good fight, I have finished the race, I have kept the faith.”

These two activities represent all that mankind could do in relation to earning God’s favour, both our inner and outer activities.

But of God who shows mercy:

This states that salvation is entirely from God, it is completely undeserved and depends entirely on His mercy; we cannot earn it in any way, by inner or outer activity.
To expand on this, Paul uses the example of Jacob and Esau, for while Jacob desired God’s favour and Esau did not value it above a bowl of soup, God’s favour was decided before they were born, before they could desire or act.
So, salvation is entirely God’s undeserved gift, not based on any merit in people.
Hence the doctrine (Sola Fide) of justification by faith: “by God’s grace alone, through faith alone, in Jesus Christ alone.”

Pitfalls of Human Doctrine

What I find interesting here is not the question of “How God chooses whom to give salvation?”, but of what that question indicates about fallen people who ask it.
When people ask about the criteria for how a winner is chosen, it is not to admire the person who hands out the prize; it’s about self-advancement, how to find the easiest way to win, with minimum effort on our part. In this verse we may ask how the winner is chosen, not to worship God as judge, but to gain his knowledge to work out what strategy we can adopt to gain the prize with minimum effort. It’s the old self-worship showing up yet again, and it reminds me of Jesus’ condemnation of the Pharisees for devising rules about God’s Law by which only they could win.

The example given by Paul of Jacob and Esau was to bring us to humility by showing salvation is not due to any human effort or desire. But this example can be misused to build fanciful human doctrine, like an intellectual house of cards, that does not serve God’s purpose of spreading the gospel, but is simply a monument to human ingenuity, the very opposite of what Paul used it for.
(May God save us from using bible study for academic self-aggrandizement.)

Personal response

Humility and thankfulness are the appropriate response to God’s provision of salvation in Jesus.
But when in thankfulness we see that the value of this gift is more precious than anything of this world, we desire it beyond anything else, so that can create a will or hunger.
And when we are humbled, all of our outward activity changes, it takes on a new direction to serve God’s will instead of our own. So, we serve with an energy driven by a debt of gratitude that we can never begin to repay, and we strive to finish the race to His glory, not ours.