Jesus is called Saviour because he saves us. And from what does he save us? A traditional answer is “from our sins”. But I’d like to give some explanation here because this formulation can get misunderstood.
You might say “He did’t do a good job, then, as we continue to repeat that we sinners”.
First of all, note that it says “He does save us”, not “He did save us”. Jesus is eternal. The process of salvation is a constant work in progress in every single human.
Then I’d add that our traditional formulation is maybe a bit too abbreviated. Jesus doesn’t save us from our sins by removing them. He doesn’t even say that we must get rid of them. He saves us from the Jewish idea about sins itself, i.e. from the idea that not doing them is a condition for making it into Heaven.
This idea was a serious theological problem of the Old Testament. That’s why you shouldn’t dive too deep into the Old Testament without your torch, i.e. you must read it through the light of the New Testament.
Jesus came to save the world from this idea. This is illustrated in the story where he heals a man born blind John 9:1-18. Paul later confirms it: “For I will be merciful toward their iniquities, and I will remember their sins no more.” (Hebrews 8:12) and “There is therefore now no condemnation for those who are in Christ Jesus.” (Romans 8:1).
This idea is one of the explanations why Christians worship the cross (see About the cross).
A hypertrophy of this idea is saviorism.
A set of Christian teachings that hypertrophies the penal substitution theory (see About the cross).
Saviorism summarizes Christian faith as follows:
Humans are sinners. We all deserve Hell. But Jesus came to save us. Those who give their life to Jesus will go to Heaven. Consequently we who follow Jesus have the holy duty to convince others to follow Jesus because otherwise they will be going to Hell.
Saviorism is based on the belief that you are in Hell because you deserve it. Seen like this, saviorism is the opposite of the Gospel, which says that we are saved through Jesus and that the Kingdom of God is already among us.
Some Bible verses about this:
“Christ Jesus, whom God put forward as a sacrifice of atonement by his blood” (Romans 3:25)
“For our paschal lamb, Christ, has been sacrificed.” (1 Corinthians 5:7)
“Christ loved us and gave himself up for us, a fragrant offering and sacrifice to God” (Ephesians 5:2)
“But as it is, he has appeared once for all at the end of the age to remove sin by the sacrifice of himself” (Hebrews 9:26)
“Christ had offered for all time a single sacrifice for sins” (Hebrews 10:12)
“Jesus Christ the righteous, and he is the atoning sacrifice for our sins” (1 John 2:2)
“In this is love, not that we loved God but that he loved us and sent his Son to be the atoning sacrifice for our sins. (1 John 4:10)