Our God is slow to anger, and for that we should be very grateful. The psalmist compares God to ruthless men who seek after his life, saying,
But you, O Lord, are a God merciful and gracious, slow to anger and abounding in steadfast love and faithfulness. (Psalm 86:15)
It's as if the psalmist is acknowledging that he deserves to be killed by these ruthless men, not in terms of human justice, but in terms of God's justice. The psalmist was a sinner, like you and me, and he deserved whatever was coming to him. But in asking God to deliver him from his enemies, he appeals to God's character.
He points out that God is merciful and gracious. God withholds what the psalmist deserves (mercy), and He gives to the psalmist what the psalmist does not deserve (grace). He abounds in steadfast love and faithfulness. God's love that He has set on His people is unfailing and not contingent upon their own faithfulness. And He is slow to anger.
Unlike us, God does not lash out in anger. He does not immediately respond to every sin with wrath. Praise be to God for that, because if it were possible, I would be slain by Him several times a minute. No, instead, He shows great patience toward us.
What mercy and grace! What steadfast love and faithfulness!
He is slow to anger toward believers and unbelievers alike. For those who do not trust in Jesus Christ, He still gives them countless blessings--food, water, oxygen, family, time etc. Rather than strike them down for their insolence, He shows great mercy.
But just because He is slow to anger does not mean He will never judge. God, being just, must and will judge at the end.
There's good news. Where He is slow to anger toward us, He was not slow to anger toward His Son. It wasn't because the Son deserved His wrath, but rather because the Son willingly took on His wrath for sinners like you and me. And now all we who trust in Jesus Christ are forgiven our sin and are saved.
Still, we ought to thank God that He is slow to anger toward us. And we ought to turn to Him in faith and obedience.