purification: the act, or the required rite, that removes what makes a person or thing unfit and restores them to acceptable standing before God
In the Bible, being clean has less to do with dirt than with fitness. A person could be perfectly washed and still be barred from the temple, and another could be scrupulously careful about washing and still carry guilt. This word names the remedy: the process that takes away whatever disqualifies someone, so that they can take their place again among God's people. It belongs to the verb "to make clean" (καθαρίζω), and where that verb describes the action being done, this word names the cleansing itself, either as an event or as a requirement to be met.
Most of its uses in the New Testament point to the purifications the Law of Moses laid down. A man healed of a skin disease is sent to the priest with an offering for his cleansing; the days of purification are counted after a birth. Around those written requirements grew a wide body of customary washing, which is why six stone water jars stood ready at a wedding in Cana and why John's followers found themselves arguing over washing practices.
Two passages carry the word past the temple courts and into the cleansing of sin itself. Hebrews says the Son made purification for sins and then sat down at God's right hand, and 2 Peter warns of a person who has forgotten the cleansing of his old sins. The choice of word is deliberate: what an offering did for a body's uncleanness, these writers claim the death of Christ has done for guilt. One word covers both, which is part of the argument.