As I was readings Psalm 51 last year throughout Lent and meditating on it, this phrase jumped out at me for the first time. Whiter than snow? Not as white as snow. Whiter.
Jesus' redemption for us is so utterly complete and perfect that before God, His children are seen to be whiter than snow. Whiter and cleaner than anything we can imagine from our experience.
Let me recommend Paul David Tripp's meditations on sin and mercy about Psalm 51. I also recommend rereading Psalm 51 with each meditation, not just the verse, because the Psalm will sink into you and give you more to think about than only one verse. It's good to read it in different translations, too, even paraphrases, to see different expressions of the original Hebrew.
Another little insight I got from Tripp is that the hyssop mentioned in verse 7 is the same kind of branch the Israelites used to paint the blood of the lambs over their thresholds so that the angel of death would pass over them on the eve of their Exodus from Egypt. Purge me with the blood of the Lamb, Jesus.
Purge me with hyssop, and I shall be clean;
wash me, and I shall be whiter than snow.