Much of the messianic expectation that developed in the intertestamental period had to do with the messiah delivering the Jews from their oppressors (the Romans), as in a political or militaristic way. This was, in the end, one of the central reasons why many of the Jewish leaders rejected Jesus as messiah, because he didn't do one of the main things they were expecting a Messiah to do. If a messiah figure didn't do that, their logic goes, he wasn't the messiah. On this side of Jesus' death, we have the benefit of understanding what they could not see, both in the words of Jesus recorded in the Gospels, but also explicitly laid out by the writer of Hebrews who says, "so Christ, having been offered once to bear the sins of many, will appear a second time, not to deal with sin, but to save (or 'bring salvation to') those who are eagerly waiting for him." (Hebrew 9:28)
I want to share some of the insights I've read from others in attempting to understand the Hebrew/1st century understanding of salvation and then examine how that might be different from our modern understanding of it.