Taharah is purification, from tahor, meaning pure. In addition to the ritual context of taharah, there is also a spiritual form that is the culmination of repentance and the goal of Yom Kippur.
"For on that day He will forgive you, to purify (letaher) you from all of your sins - you will be purified (titharu) before the Lord." What kind of taharah is Leviticus 16:30 talking about?
According to Rav Joseph Soloveitchik, you reach taharah when you have not only overcome your weaknesses - for that you receive kaparah (forgiveness) - but when have made changes in your life so that you will never regress to your former ways. The Talmud gives the example of a gambler destroying his dice and a pigeon racer breaking his bird traps (Sanhedrin 25b) .
Rabbi Akiva famously declared, "Fortunate are you Israel! Who is it before whom you become tahor? And Who is it Who makes you tahor? Your Father Who is in heaven" (Talmud, Yoma 8:9).
Ever the optimist, Rabbi Akiva focuses on the joy of taharah, the very fact that it is possible and that the process offers us a chance for a new closeness to God.