What does Psalm 65:3 mean?

In this verse David praises God for atoning for his sins and those of the nation. He calls these sins "iniquities" and "transgressions." Iniquities are something warped, perverted, or deprived of God's goodness. This describes the fallen human nature. Human sin is so ingrained that it's impossible for any person to personally overcome (Psalm 38:4; Romans 3:20). Transgressions are violations of some boundary or rule. Here, David uses both personal and group terms: he is a sinner, and Israel is a sinning nation.

However, David recognized that God provides atonement: a way to make amends for sin. As the apostle Paul observed, "Where sin increased, grace abounded all the more" (Romans 5:20). David understood that he could approach God in prayer only as a forgiven sinner. On the Day of Atonement that occurred once a year, Israel's high priest shed the blood of a bull and sprinkled it on the altar and mercy seat to symbolically cover his sins and his family's sins. He did the same with the blood of a goat for the nation's sins. Yet the Old Testament law required this to be repeated every year. By contrast, by the once-for-all sacrifice of His blood on the cross, Jesus provided forgiveness forever for those who believe on Him (Hebrews 7:26–27; 9:11–14; 10:10–14).