What precisely is the salvation offered me?

During a dinner hosted by a friend, in the context of a casual discussion about church attendance, a guest said, ‘I am satisfied that Jesus died on the cross for my salvation.’ There was no further development of that thought.

What is salvation? Is it unique to Christians? Did Christ offer this salvation? Or, did he only say ‘Only through me shall ye know God’? Was he then not referring to the one god of all mankind he proclaimed (as had others elsewhere on the globe in earlier times in history), as distinct from the regional gods of his peoples?

In any event, does salvation refer to the future of one’s soul after death? Accepting that our souls are who we are, with our bodies of form and substance providing cover (or a vehicle) while on Earth, a Hindu can accept that the soul, after bodily death, would spend some time in that temporary home, the spirit realm; rebirth would subsequently occur.

The New Ager can apparently expect to be assessed and subsequently guided to a new life.

To the Hindu, reincarnation and karma (the destiny path) would be, as I understand it, automatic, the law of cause and effect (possibly in the form of a Court of Cosmic Justice) being the operative well-oiled mechanism; no judgement/punishment, or assessment/guidance, would be necessary.

To Christians, would the idea of salvation of one’s soul become relevant only in the context of one’s Afterlife being decided after judgement? If so, by whom? Would possible punishment be prospective? If so, to where or what? Would this idea reflect an authoritarian, prescriptive priesthood or religious institution?

Is this why I have not found any regular church-attending Christians who are able (or willing) to tell me where they expect to go after death? Is this also why so many of them are afraid to die?