The concept mentioned here has appeared in the Old Testament (Proverbs 10:12). Peter’s sentence is open to multiple interpretations:
God’s love (for me) covers my sins.
My love (for God) covers my sins; see Luke 7:47.
My love (for the neighbour) covers the neighbour’s sins; see Matthew 18:27.
Grammatically and theologically, all three are possible. But the flow of thought in this letter requires us to understand that Peter had the third option in mind. Earnest love for the brother means that you choose not to stumble over his weaknesses and sins but instead downplay the wrong and forgive. Within the circle of the saints there is to be great patience with one another even as the Lord displays great patience and mercy in the face of our sins against him. This forbearance enhances a healthy communion of saints.
8 Above all, keep loving one another earnestly, since love covers a multitude of sins.