Grace has been described as a sphere of constant forgiveness. Undeserved, unmerited favor. Being shown love, even when we are unlovable. Grace is one blessing after another that we don't deserve.
The life of Paul is an amazing example of God's Grace. After years of persecuting the followers of Christ, Paul (or Saul as he was called at the time), encountered Jesus on the road to Damascus and became God's chosen instrument to proclaim His name all over the world. (Acts 9)
In Paul's first letter to Timothy, he describes his transformation like this, "I thank Christ Jesus our Lord, who has given me strength, that he considered me trustworthy, appointing me to his service. Even though I was once a blasphemer and a persecutor and a violent man, I was shown mercy because I acted in ignorance and unbelief. The grace of our Lord was poured out on me abundantly, along with the faith and love that are in Christ Jesus. Here is a trustworthy saying that deserves full acceptance: Christ Jesus came into the world to save sinners - of whom I am the worst. But for that very reason I was shown mercy so that in me the worst of sinners, Christ Jesus might display his immense patience as an example for those who would believe in him and receive eternal life." (1 Timothy 1:12-16)
Let Paul's encounter and transformation be an encouragement to you. No matter what you've done, God will forgive you. No matter what you've been through, God has a plan for your life that can bring Him glory. Like Paul, once we have repented and accepted the mercy and love of Christ, we must strive to continue to grow in grace. This does not mean we need to do things to try to earn more grace. God's grace never increases or decreases; it is infinite, impossible to measure. To grow in grace means that we should continually grow in our knowledge of and relationship with God, maturing and becoming more and more like Him as we surrender to Him.
The more we rely on Him, the stronger His power in us will be. Grace doesn't take away our troubles, trials or temptations, but it does give us the strength to overcome them.