"As for the person who hears my words but does not keep them ..." (John 12:47)

"As for the person who hears my words but does not keep them, I do not judge him. For I did not come to judge the world, but to save it." (John 12:47) 

How does Jesus 'save the world'?

If we look at Jesus' statement in context, we can see that saving the world is connected to hearing and keeping his "words."

What does it mean to "keep" Jesus' words?

"Words" is being translated from the Greek word ῥῆμα (rhēma). According to Thayer's lexicon, this would mean, in context, "my teachings," or "instruction," or more specifically, "to deliver the whole doctrine concerning this life, i.e., the life eternal."

Yes, Jesus is referring to the wisdom that he has been presenting to his followers. He is asking his followers to carefully listen to his teachings, and then follow them.

This is what Jesus meant by saving the world. Jesus isn't teaching that he will save the world by dying on the cross. If this was his message then he wouldn't need to ask his followers to hear his teachings and follow them. He would have told them to just wait until he dies on the cross and then they'll be saved.

But Jesus never says this.

What was Jesus mean by 'keep them'?

Jesus is referring to his teachings. The term, "words" is translated from the Greek word ῥῆμα (rhēma), which means "speech, discourse" according to Strong's lexicon.  According to Thayer's lexicon, it would relate to "doctrine," or "instructions." 

This means that Jesus is talking about those who hear his teachings but don't follow them. 

Jesus used his words to teach. He stood in front of groups of people - large groups and small groups - and he spoke to them. He taught them. Why would he spend so much effort if he was going to save them by dying on the cross?

Just in the book of John, we find the records of over 125 different teachings by Jesus. While there is a significant crossover, we find dozens more in the other three Gospels. Then we find so many other teachings by Jesus in the recently discovered Lost Gospels of Jesus. Between all of these Scriptures, we find the records of years of teachings. Jesus spent years walking the countryside teaching people.

What were his teachings about? They were primarily about God. Jesus taught us to love and serve the Supreme Being:
"Not everyone who says to me, 'Lord, Lord,' will enter the kingdom of heaven, but only he who does the will of my Father who is in heaven." (Matt. 7:21)
Doing someone else's will requires first wanting to do someone else's will. We must desire to please that other person.

Let's consider Jesus' most powerful and important words. His most important instruction was:
“‘Love the Lord your God with all your heart and with all your soul and with all your mind.' This is the first and greatest commandment." (Matt. 22:37-38)
Hearing (or reading) these words is one thing. It is one thing to acknowledge that Jesus wants us to love God. But keeping these words is an entirely different matter.

Keeping Jesus' words, "Love the Lord your God with all your heart..." means to cherish God above all else. For those who do not know God, it means to search for God and reach out to God will all our hearts - with prayer, praise and study. And for those who have come to know God through God's representative, it means to work to please Him.

And Jesus was trying to teach love for God to those who did not love God:
"I know that you do not have the love of God in your hearts." (John 5:42)
We can't love someone we don't know. This means that we have to come to know who God is. We have to understand His personality. This is why Jesus prayed to God:
"Now this is eternal life: that they may know You, the only true God, and Jesus Christ, whom You have sent." (John 17:3)
This part of Jesus' prayer to God clearly illustrates that the Supreme Being sent Jesus so that Jesus could help us come to know God.

Jesus' "saves" through his teachings - his words - that teach us how to re-establish our loving relationship with God, and return to Him.