Grace:  Grace expresses the undeserved favor that God shows to people - specifically to sinners, in forgiving their sins and incorporating them into His family as sons and daughters.  The concept of grace is not birthed out of the New Testament but in fact exists in the Old Testament as well.  God's favor toward both Noah in Genesis 6:8 and toward Moses in Exodus 33:12-13 were undeserved.  That is grace. But I do agree with author Philip Yancey when he writes about trying to define grace, "Grace can be dissected as a frog but the thing dies in the process and the innards are discouraging to any but the pure scientific minds".  We best understand grace in the story of people's lives.  When you feel your worst, you're dirtiest.  When you know you've done something wrong or even evil.  Were do you go, what are you drawn to?  Is it the church?  Is it Christians that you know?  Jesus is our best living and breathing example of grace.  The worse people feel about themselves, like the woman caught in adultery or the crooked, hated, businessman Zacchaeus, the more likely they are to see Jesus as a refuge.  That is grace experienced. 

Justification:  The action of God in not adding up sins against those who have committed them but rather forgiving them and entering them into an incredible relationship with himself.  This is God's act of making us right before himself and it's possible because of Christ taking on our sin on the Cross. 

Having understood these two terms, let's use Romans 4:4-5 to help us understand the distinction between faith and works.

Romans 4:4-5

Now when a man works, his wages are not credited to him as a gift, but as an obligation. However, to the man who does not work but trusts God who justifies the wicked, his faith is credited as righteousness.

To live by works is to have the mindset of an employee.  God is the boss; I am his hired hand, the employee.  If I do what God wants, then God, because he is the employer and I am the employee, owes me something.  In this case, he "owes" me entrance to the other side of eternity.  Or a good life full of money and health.  But faith is the person who trusts God knowing that God is the creator, that God is Holy. No sin, no evil, no darkness are within him. But because God is love at the core of his character, he out of love showered his grace upon us, and in doing so has credited our life as right, as "righteous" before a Holy and Just God. 

So when we do good works, or we follow the law, or as in the case of the 1^st century church, get circumcised, God still doesn't owe us anything. But he out of love, not out of obligation, took our place on the cross.  That is good news; that is the Gospel.  Paul is so upset because the judaizers required circumcision to come to Christ and to follow Christ. Clearly this implied that the cross was not enough.  And if circumcision or any other works doctrine could save us and connect us to God, then we would boast in ourselves and in doing so take away that which God always requires and desires - his own glory, his own recognition in our lives and in the entire world. He has done all the work.  That is why in verse 12 of Galatians 5, Paul would rather these judaizers harm themselves physically than teach circumcision to followers of Jesus Christ. 

Soon after Paul wrote this letter to the churches in Galatia he took a journey over this issue to the ruling council in Jerusalem that included the original Apostles (Acts 15:1-35 ). 

Some men (converted Pharisees) were teaching the Gentiles, "Unless you are circumcised, according to the custom and Law taught by Moses, you cannot be saved".  This is essentially what Paul addressed in Galatians.  Paul and Barnabas took the trip to Jerusalem to see what the Apostles and Elders had to say about this question.