What is the importance of fasting in the month of Dhu al-Hijjah and on the Day of Arafah?

Fasting on the first nine days of Dhu al-Hijjah is considered as mustahab. One may fast for the whole or for a few of those days as s/he wishes.

The Day of Arafah, which is the ninth day of Dhu al-Hijjah, has an important place in Islam. Regarding fasting on this day, Prophet Muhammad (saw) said, “It is hoped from Allah that fasting on the day of Arafah may atone for the sins of the preceding and the coming years.” (Muslim, Siyam, 196-197). However, for those who are performing hajj at this time, not fasting is more appropriate in order to not delay the required worships or have hardship and exhaustion (Abu Dawud, Sawm, 64).

Source: Presidency Of Religious Affairs The Turkey, High Board of Religious Affairs FATWAS

What is The Importance Of The First Ten Days Of The Month Of Dhu Al-Hijjah?