Christians call Jesus Christ "our saviour", or simply The Saviour - but it is not clear to secular modern people what we mean by this; indeed, I believe that the meaning (or emphasis) has changed over the centuries, because Christ did not save us from just one bad fate; but from many, many bad things - and different people at different times feel themselves in need of different savings: so that what I understand Christ as saving-me-from may not be your understanding.
At the time of his ministry and for many centuries, Christ was understood as saving us from death; and by 'death' people meant that the soul would usually endure in a (literally) nightmarish underworld (Sheol, Hades etc) where we would persist forever as demented, gibbering, desolate ghosts.
In effect, death meant death of 'the self' - death of consciousness and the will - but not an end to existence.
Christ was also saving us from sin; and it seems clear that through most of history Men felt this to be necessary: felt that we absolutely needed to be saved from our sins; and that if we were not saved from our sins, then we would be tormented by them forever.
But modern Western Man does not feel himself in need of saving from death - because he regards death as extinction and therefore the end of suffering (not death as the doorway to endless suffering, as in the past).
And modern Man does not feel he needs to be saved from sin, because he regards 'sin' as an arbitrary cultural category - and Modern Man has redefined many sins as virtues, virtues as sins.
So in effect, Modern Man 'saves himself' from sin by promoting, enforcing, and believing, legislation and propaganda to abolish any sin he cannot stop or does not wish to stop; and making new sins from whatever threatens the continuation of this process.
But Modern Man still needs to be saved - he needs to be saved from meaninglessness, purposelessness, existential isolation, alienation, and nihilism (the sense that all truth, beauty and virtue are 'relative'; that values are 'subjective', that nothing is really-real).
Modern Man needs to be saved from the retrospective pall cast by the meaning-destroying pseudo-reality of death-as-extinction; and the nothingness of a world where profundity is repeatedly dissolved and remade, and where Man is become a mere conduit for ever-changing psychological manipulations.
Another thing Man always has needed saving-from is suffering; the suffering of this world.
And Christ saves us from this suffering in two ways, at two levels. In the first place he offers a significant, albeit partial, alleviation of suffering in this world - mainly by putting suffering into a perspective of eternal hope.
An analogy would be the suffering of childbirth. Childbirth can be agony: in a purely physical sense childbirth may be as painful as torture - but the suffering is put in the perspective of a parent participating in the birth of a child and this makes a very big difference. Indeed, the perspective utterly transforms the meaning of pain, and drastically reduces the suffering.
And secondly, the long-term effect of suffering is likewise transformed by Christ - because there is the prospect of complete healing from all the ill effects of suffering at the resurrection.
So all earthly sufferings are re-framed by Christ as temporary.
Christ is still our Saviour, as before; but now Christ is perhaps primarily (upfront) most-often our saviour from the void.
Christ is now, mostly, our saviour from the denied but pervasive existential terror that nothing really matters.
With salvation it is not a matter of either/ or; but a matter of all-this-and-more.
Because death, sin, suffering and alienation are all facets of the same evil fate - therefore Christ is The Saviour.
However, maybe when we state this great truth to non-Christians, we need to consider what they personally most need saving-from.