What is God's mercy?
Mercy is giving something to someone that they don't deserve. When people come to faith, trust and salvation in Jesus Christ, the punishment for their sins is forgiven, all paid for by Him on the cross. This is God's greatest mercy. A believer does not have to suffer the penalty of eternal punishment in the lake of fire. Whenever someone falls short and sins, if we confess our sins to the Lord we are forgiven. His compassion and forgiveness for us are extended by His mercy and love.
Mercy is also something that everyone should show to those around them. If you do something wrong you want the person you wronged to show you mercy: so do unto others as you would have them do to you, as taught in Mark 12.31 and Luke 6.31.
" But God, who is rich in mercy, because of His great love with which He loved us, even when we were dead in trespasses, made us alive together with Christ (by grace you have been saved), and raised us up together, and made us sit together in the heavenly places in Christ Jesus, that in the ages to come He might show the exceeding riches of His grace in His kindness toward us in Christ Jesus. For by grace you have been saved through faith, and that not of yourselves; it is the gift of God, not of works, lest anyone should boast."