"Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me." John 14:6 (KJV).
Salvation is the term used in the Bible, churches and elsewhere to mean "made acceptable to God" because sin has been removed or forgiven. Salvation in Jesus, sometimes also referred to as the Christ or Christ Jesus, does both - removes sin and brings forgiveness. Salvation is a gift from God, offered freely to everyone. But, only those persons who accept the truth of Jesus' birth, life, death and resurrection, and repent (meaning to turn away from things that God opposes and not continue in those things) are forgiven of their sins under God's plan of salvation through His grace.
True, God did deliver 10 Commandments (Deut 5:6-7 >) to Moses as rules for His people, the Jews, to obey - but the reality is that no one can live up to them. And no one ever could; they were intended to show things that honored God and pleased Him, for people to live by and thus show their respect and worship of Him. Those same Commandments are the basis for every law, of every nation and society, that ever has or ever will exist.
Again, we are made in His image, for His good pleasure, for His glory. So, why doesn't God simply remove the separation from Himself with mankind that sin creates, and extend salvation to everyone?
Because we are not puppets, controlled by a master who does with us whatever he wishes, whenever he wishes - but that's only one reason why. Remember, we were born with the ability to choose things for ourselves - free choice - and to forgive the sin of everyone with a wholesale action means we also lose that freedom to choose for ourselves. God loves us too much to do that; He loves us so much that He gives us the right to reject Him and His glory. He made us to be free, and we truly are free to choose what we wish; God's plan of salvation proves that, and we have the right - God-given - to accept it or reject it. It's just that simple.
But He proves His love for us by His Word and His actions: "For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life." John 3:16
Think about it: if God could, would, simply remove sin that separates us from Him, why would Jesus have had to suffer and die on a cross for the sins of the world? Jesus truly is the only way to God.
But why do we need salvation? Because salvation is the only thing that will save us from spending all of eternity separated from God - in a place called Hell. Salvation removes the stain of sin from our immortal soul, and presents us as pleasing to God - Who can not have fellowship with sin in any form. That is why He had to turn from the sight of Jesus dying on the cross for the sins of the world; in that moment, Jesus became the sacrifice for all the sin that separates anyone from favor with God.
Through salvation, we are made clean through Jesus' sacrifice and blood - the same Jesus sent from heaven by God for the redemption of everyone who accepts His Son as Lord and Savior.