In this penitential Psalm, David begs the Lord to clean him, so that he will be truly clean. The verb translated by the ESV as “purge” (חטא in the piel) is a word associated with making a sin offering or preparing an altar for an offering )Lev 8:15, Ezek 43:22(. The verb is therefore chose to emphasize the fact that David wants to be made fit for worship once again. In his current state, he is unclean and cannot participate in joyful worship at the Tabernacle. The result of being purged with hyssop is that David will be clean, ritually purified (טהר). In the Qal, this verb usually indicates that something or someone is ceremonially clean.
To be “purged with hyssop” may be an allusion to Exod 12:21-22, bunches of hyssop were tied together and used to brush the blood of a lamb on the doorposts prior to the Passover. But hyssop was used to purify lepers as well ( ABD 2:812). Perhaps that is the point here as well. Like a leper, David sees himself as in need of ultimate purification.
When the Lord cleanses him, David’s purity will be “whiter than snow.” The second verb for washing in verse 7 is used for washing and bleaching a garment. The verb appears frequently in Lev and Num for ceremonial cleanliness. It is easy to hear this metaphor through a modern lens, we just add a bit of detergent to the wash and clothes are bright white. But that is not the case in the ancient world. Caustic chemicals were used and clothing must be beaten in order to clean it thoroughly. The verb here (כבס) refers to “treading, kneading and beating” clothing (HALOT). I have included an image here of an Egyptian washing bat. This is a rare find since common implements like this would fall to pieces after long use and be discarded. “Depictions of laundrymen at work show that the items being washed were treated to violent beating and mangling by twisting” (Digital Egypt for Universities, see also Real Life at Deir el-Medina). It is impossible to know if clothing was washed white in the same was in Ancient Israel, but is likely that the process was similar.
David uses this metaphor in recognition that to be clean he will indeed need to suffer, beaten like a garment which is being washed with the laundryman’s bat. Mal 3:2 uses a similar metaphor for spiritual renewal, it is like a refiner’s fire or a fuller’s brush. David has already said that he was born in sin and therefore is unable to be pure before God – Only God and do something which changes him and makes him really pure and right before God.
That David would ask for his joy (verse 8, 12) to be restored indicates the depth of his anguish for his sin and the punishment he is enduring. In verse 8 his bones are broken, the verb is “crushed” (דכה, a rare word which only appears here and Ps 44:20 in the piel, in the Qal in 51:17, a broken heart). The cognate noun refers to the dashing of waves against the shore, a relentless pounding which likely is part of the same metaphor as cleansing with laundryman’’s brushes.
The vocabulary used for joy in these verse are often associated with joyous occasions such as weddings (Ps 45:7) or the Exodus (Ps 104:43), worship (Zech 8:19) or the presence of the Lord (Isa 35:10). Anticipating the end of the psalm, perhaps David has in mind a restoration to worship, after he has been cleansed by the Lord he can once again enter into the joyous celebration of the Tabernacle / Temple in the presence of the Lord. Remember David leading the worship of Israel as the Ark was installed in Jerusalem – his unbridled joy and enthusiasm was shocking and undignified. He looks forward to being free from the guilt of his sin so that he can experience the freedom to worship God in such a joyous way.