Although most of the other penitential psalms are communal prayers, this psalm is expressed as an individual cry, Have mercy on me, blot out my transgressions, wash me, and purify me.
And I can ask this of God because mercy is what God is like, because mercy befits God's faithfulness, because God is abundantly compassionate
Sometimes, we need reminders that we are sinning. And, sometimes, we are so burdened by our sins that we need reminders that God is compassionate.
We can pray Psalm 51 when we recognize that we need forgiveness, that we want forgiveness:
Let me hear joy and gladness; let the bones that you have crushed rejoice.And we can pray Psalm 51 when we want what forgiven people have--restoration
Hide your face from my sins, and blot out all my iniquities.
Create in me a clean heart, O God, and put a new and right spirit within me.
Do not cast me away from your presence, and do not take your holy spirit from me.
Restore to me the joy of your salvation, and sustain in me a willing spirit.