This passage occurs in the Narrative Lectionary, Year 1 (most recently Oct 19, 2014); it also occurs many years in the Revised Common Lectionary during Lent.
Summary: There are rich theological themes in this Psalm 51. For my blog this week, I try to get into some the words, which are rich in imagery in the Hebrew. Hopefully these descriptive words can be a means to get into the Psalm (and accompanying story of David, Bathsheba and Nathan). As a side note, I've always seen the fullest expression of Gospel in this passage in the existence of the Psalm 51. God turned David's sin into something that was enduring and lasting. His child died, but his words of lament have comforted people for centuries.
נביא ("Nivea" meaning "prophet", 51:1 (intro to Psalm): The word prophecy often means prediction in modern popular imagination and film (Harry Potter/Star Wars). The prophets in the Bible did not predict the future. Rather, they spoke the word of God, which often included future possibilities for judgment or promises of blessing. But the main job of the prophet was to speak the Word of the Lord to the present situation, in this case, a king who had sinned badly. Very badly.
נתן ("Nathan", name of the prophet, 51:1 (intro to Psalm): The prophet's name "Nathan" means gift. Even the harsh words of God are a gift to David here in that he calls David to repent, to have a restored relationship with God. When we deny calling 'sin' 'sin' we deprive people of the gift of forgiveness and repentance.
רחמים ("rakamim" meaning "compassion", 51:2) The origin of this word רחם meaning is womb. In the plural it means compassion; this is clearly feminine way of thinking about God's love; it is like a woman's care born in her womb.
מחא ("makha" meaning "wipe", 51:2;9): As the TWOT points out, almost every time this verb shows up in the Hebrew Bible, it is significant. For example, God will wipe out the earth with a flood; God will wipe away every tear in the eschaton (Isaiah 25:8). The literal action means: "Erasures in ancient leather scrolls were made by washing or sponging off the ink rather than blotting. " Literally erase away, expunge! So that when God reads the book of life, he reads them no more.
כבס ("kabas" meaning "launder", 51:3;7) TWOT: "to make stuffs clean and soft by treading, kneading and beating them in cold water...it is used always for clothing, 'to launder'"
טהר ("tahar" meaning "cleanse, purify", 51:3;7) In Hebrew, this word is associated with pure metals (especially gold); it is often associated with ritual and ceremonial cleansing and furthermore, cleansed items used in worship. You could go a couple of ways here: First, that God's cleansing is like removal of dross from metal -- getting rid of the crap in our lives that we might be pure. Second, you could argue that the cleansing has a purpose (to be used in worship and service to God). Third, you could argue that ultimately forgiveness neats a ritual cleansing, including through washing with water or blood.
חול ("khul" meaning "twirl" translated here as "born", 51:5) from the moment the person begins writhing, twirling, dancing, moving, even in pain, they are born with sin.
אמת ("amat" meaning "faithfulness" or "truth", 51:6) What is it that God desires? It is not simply truth as in a true statement, but faithfulness. Something beyond propsitional truth is desired here. We could do a lot more here, but the NET translates this nicely with integrity.
ברה ("barah" meaning "create" 51:10) Just a reminder that this verb is only associated with God as the subject. Humans can fairly be described as co-creators in the sense of we can imagine, build, make, name...but we cannot create life; nor can we create a new heart.
קדש ("kadesh" meaning "Holy" 51:11) This is the only time in the Old Testament we have an unambiguous reference to the Holy Spirit. The NRSV does not do Christians justice when they translate the words with lower case holy spirit.