What is grace?

Grace is one of those things that is better shown than defined.  Nevertheless, some common definations are: God's unmerited favour toward those who have merited his disfavour; and God's Riches At Christ's Expense. These are good but remain inadequate. 
Luke 24:47 records the Lord's words  to his disciples before he ascended to the Father. He told them to proclaim repentance and forgiveness of sin in his name to all the nations beginning in Jerusalem.  Beginning in Jerusalem are some of the most gracious words ever spoken. Why? It was in Jerusalem that the Savior was betrayed.  Those people who worshiped Jesus as he rode into the city were some of the same ones that cried "crucify him" to Pilate. These wretches mocked and scorned the Lord of Glory. As he hung on the cross they ridiculed even more.  In Acts 2, Peter preaches and says that these people killed Jesus.
So where is the grace?  Those same murderous people were the first to hear the gospel. Further,  three thousand were converted in one day. That's grace. The disciples were to begin preaching in the very place in which Christ was crucified to the same people that killed him. Oh, marvelous matchless grace!
God is still gracious. We too enjoy him lavishing his grace on us through Christ our Savior. Grace upon grace upon grace. Everything on this side of heaven is grace. We don't deserve anything good or beneficial from the hands of God.  We deserve hell and damnation. But praise him, worship the God of all grace.
To give credit where it is due, John Bunyan preached a sermon entitled The Jerusalem Sinner Saved. I have adapted this into an illustration of God's grace. Read it for profit. Read it to better understand the amazing grace of God.