In order for the language of being "saved" to make sense one has to understand what we are being saved FROM. There has to be a before and after scenario. We are saved from the wrath of God. Those without faith in Christ are described as children of wrath.

Consider this passage that uses the language of being "saved" including some details on our original position before God, the change that happens, and our final standing after salvation as well as the key operative bits on how that actually happens:

Ephesians 2:1-9 (ESV)
1 And you were dead in the trespasses and sins 2 in which you once walked, following the course of this world, following the prince of the power of the air, the spirit that is now at work in the sons of disobedience— 3 among whom we all once lived in the passions of our flesh, carrying out the desires of the body and the mind, and were by nature children of wrath, like the rest of mankind. 4 But God, being rich in mercy, because of the great love with which he loved us, 5 even when we were dead in our trespasses, made us alive together with Christ—by grace you have been saved—6 and raised us up with him and seated us with him in the heavenly places in Christ Jesus, 7 so that in the coming ages he might show the immeasurable riches of his grace in kindness toward us in Christ Jesus. 8 For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, 9 not a result of works, so that no one may boast.

That wrath was metered out on Christ (Isaiah 53:5) and by bearing this punishment and separation from the Father he claimed the right to make us Sons. He transferred us from the domain of darkness into the light.

Colossians 1:1-14 (ESV)
11 May you be strengthened with all power, according to his glorious might, for all endurance and patience with joy, 12 giving thanks to the Father, who has qualified you to share in the inheritance of the saints in light. 13 He has delivered us from the domain of darkness and transferred us to the kingdom of his beloved Son, 14 in whom we have redemption, the forgiveness of sins.

Returning the the language of Ephesians above, "being saved" means being made alive, to be raised up with Christ. A few verses after the Colossians passage above it talks about how God reconciled us to himself through Christ.

To "be saved" thus means to be rescued from the wrath of God, made alive in Christ and reconciled to the Father. The pre-salvation scenario thus has us as an object of God's wrath, the post-salvation scenario has us as objects of His affections and co-heirs with Christ.

In order for the language of being "saved" to make sense one has to understand what we are being saved FROM. There has to be a before and after scenario. We are saved from the wrath of God. Those without faith in Christ are described as children of wrath.

Consider this passage that uses the language of being "saved" including some details on our original position before God, the change that happens, and our final standing after salvation as well as the key operative bits on how that actually happens:

Ephesians 2:1-9 (ESV)
1 And you were dead in the trespasses and sins 2 in which you once walked, following the course of this world, following the prince of the power of the air, the spirit that is now at work in the sons of disobedience— 3 among whom we all once lived in the passions of our flesh, carrying out the desires of the body and the mind, and were by nature children of wrath, like the rest of mankind. 4 But God, being rich in mercy, because of the great love with which he loved us, 5 even when we were dead in our trespasses, made us alive together with Christ—by grace you have been saved—6 and raised us up with him and seated us with him in the heavenly places in Christ Jesus, 7 so that in the coming ages he might show the immeasurable riches of his grace in kindness toward us in Christ Jesus. 8 For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, 9 not a result of works, so that no one may boast.

That wrath was meted out on Christ (Isaiah 53:5) and by bearing this punishment and separation from the Father, He claimed the right to make us Sons. He transferred us from the domain of darkness into the light.

Colossians 1:1-14 (ESV)
11 May you be strengthened with all power, according to his glorious might, for all endurance and patience with joy, 12 giving thanks to the Father, who has qualified you to share in the inheritance of the saints in light. 13 He has delivered us from the domain of darkness and transferred us to the kingdom of his beloved Son, 14 in whom we have redemption, the forgiveness of sins.

Returning to the language of Ephesians above, "being saved" means being made alive, to be raised up with Christ. A few verses after the Colossians passage above it talks about how God reconciled us to Himself through Christ.

To "be saved" thus means to be rescued from the wrath of God, made alive in Christ and reconciled to the Father. The pre-salvation scenario thus has us as an object of God's wrath, the post-salvation scenario has us as objects of His affections and co-heirs with Christ.