“So, what exactly is the purpose of good works in the Christian life?”
1) Is it to gain a right standing before God or be accepted by Him? Is it to try and appease His infinite, holy, and just wrath against our sin? Is it to earn our own salvation from the right wages of our sin, spending an eternity in conscious bodily torment as the just penalty for our offense against God?
No, because salvation cannot be earned. Rather, it is a free gift of God. The Word of God reads:
“For the wages of sin is death, but the free gift of God is eternal life in Christ Jesus our Lord.” – Romans 6.23
“For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, not a result of works, so that no one may boast.” – Ephesians 2.8-9
2) Does this question seem irrelevant? Are works to even play a part in the Christian life since salvation is by grace?
Yes. Works do play a part. In fact, they are a vital part of the Christian life, as they serve to validate the Christian faith:
“What good is it, my brothers, if someone says he has faith but does not have works? Can that faith save him? … So also faith by itself, if it does not have works, is dead … For as the body apart from the spirit is dead, so also faith apart from works is dead.” – James 2.14-17, 26
3) Is it to make much of the Christian? Is it to make moral the pagan man? Is it to clean up that which would otherwise be filth? Is it to exalt the Christian that he might appear good before others? Is it to puff-up the Christian in order to look down his nose at others?
No. While genuine salvation does cleanse, it is not about spreading the cause of morality or elevating self-image. Rather, it is about making much of God:
“In the same way, let your light shine before others, so that they may see your good works and give glory to your Father who is in heaven.” – Matthew 5.16
So, what is the purpose of good works? To point those around us to the Father. This can be evangelistic if we find ourselves in the company of non-believers or it can be for the purpose of building up the body of Christ when in the company of fellow believers. However, it is always to validate the profession of faith we have already made and affirm the salvation we have already freely received, to the glory of God, the Father.