Saved from what?
It has become a cliche in the Christian society to say “I am saved”. But what are we really saved from? What does it really mean to say “I am saved”? What are we saved from? Are we saved from ourselves, sin or satan? Though we are saved from sin, ourselves and satan, that's not what we are ultimately saved from.
Why would man have a need to be saved? The answer is in the state of the relationship between man and God. What is the relationship between God and the unregenerate man like? Are we buddies with God or are we His enemies?
God made man, gave him a law to keep and man broke it. And from then on man has been rebelling against God. But since the wages of sin is death (Rom. 6:23) and God is a just judge (Psa. 7:11), He must punish the sinner. This means that “God is angry with the wicked every day.” (Psa. 7:11). So God and the unregenerate man are not buddies, no, they are enemies. God hates sin and the man who sins (cf. Psa. 5:5) and man hates God (cf. Rom. 8:7).
You're probably asking, doesn't “God hate sin and love the sinner”? Well, that's not what the Bible teaches. “The LORD tests the righteous, but the wicked and the one who loves violence His soul hates.” (Psa. 11:5) (cf. Psa. 5:5, Psa. 7:11). God doesn't send sin to hell, He sends the sinner to hell.
So what does God do to God-haters like us? Well He must pour out His wrath upon us. He must send each and everyone of us to hell to suffer His wrath for eternity. But man keeps accumulating wrath for himself (cf. Rom. 2:5) and doesn't want to fix the relationship.
The good news
“But God demonstrates His own love toward us, in that while we were still sinners, Christ died for us.” (Romans 5:8)
In the midst of God's hate for sin and sinners, He sent His Son to reconcile man to Himself. Jesus Christ, the eternal Son of God, stooped down from heaven to earth to reconcile man back to God. Jesus came to earth and fulfilled the righteous requirements of God's law in our place (cf. Rom. 8:4) and on the cross He bore our sins. Jesus drank the cup of God's eternal wrath (cf. Mar. 14:36) on the cross. He suffered the hell that we should suffer in hell on the cross. And He appeased God's wrath (see propitiation). “There is therefore now NO CONDEMNATION to those who are in Christ Jesus, who do not walk according to the flesh, but according to the Spirit.” (Rom. 8:1). God can forgive the enemy who turns from His sins and puts his faith on Him.
“For if when we were enemies we were reconciled to God through the death of His Son, much more, having been reconciled, we shall be saved by His life.” (Romans 5:10)
If you turn from your sins and turn to and trust in God, He will wash you from your sins and make you clean (Psa. 51:2), He will cast your sins as far as the east is from the west (Psa. 103:12) and make you as white as snow (Isa. 1:18). He will also credit Christ's righteousness to you (2 Cor. 5:21). He will adopt you as His son and love you with the same love He loves His Son (John. 17:23). He will take away you heart of stone and give you a heart of flesh (Eze. 36:26-27) that loves Him and hates sin (see regeneration). And He will free you from the bondage of sin (Rom. 6:7).
“God saved you for Himself; God saved you by Himself; God saved you from Himself.” – Paul Washer
We are saved from the wrath of God. Jesus appeased the wrath of God for all who believe in Him when He died on the cross. God offers forgiveness of sins and reconciliation through His Son Jesus Christ. But God's wrath abides on all who don't believe in Him and they store up more wrath for themselves daily, and it will be poured out on them in hell for all eternity.
Soli Deo Gloria