Grace and Mercy
Grace is defined as undeserved favor, therefore showing grace means being kind to someone when they are not deserving of that kindness. We as humans can show grace to one another, but the grace that we, as Christians are most interested in is the grace that God has shown to us.
God's greatest act of grace was gving up his son to die that we might be redeemed from our sins. There was nothing that we did or could have done to deserve that grace.
Here God demonstrates his love for us, because if when we were sinners, the Messiah died in our place, 9 how much more therefore, would we all the more be justified now by his blood and be saved from wrath by him? 10 For if when we were enemies, God was reconciled with us in the death of his Son, how much more therefore, in his reconciliation, shall we live all the more by his life? (Romans 5:8-10)
As sinners and enemies of God we were separated from God without a way to undo what we had done and deserved nothing but destruction, but God, as an act of grace, provided his son to die for us, that we could be reconciled with God, justified, and saved from what we deserved.
The words "Grace" and "Mercy" are often used together because they are so closely related. Grace can be said to be showing Mercy. So, from the definition of Grace above, we see that Mercy is undeserved favor.