The ninth day of Dhul-Hijjah is the day of ’Arafah, since it is on this day that the pilgrims gather at the mountain plain of ’Arafah, praying and supplicating to their Lord.
It is mustahabb (highly recommended) for those who are not pilgrims to fast on this day, since the Prophet (sallallaahu ’alayhi wa sallam) was asked about fasting on the day of ’Arafah, so he said, “It expiates the sins of the past year and the coming year.” 
Likewise, the Prophet (sallallaahu ’alayhi wa sallam) said, ‘There is no day on which Allaah frees people from the Fire more so than on the day of ’Arafah. He comes close to those (people standing on ’Arafah), and then He reveals before His Angels saying, ‘What are these people seeking.” 
Imaam at-Tirmidhee (d.275H) – rahimahullaah – said, “The People of Knowledge consider it recommended to fast on the day of ’Arafah, except for those at ’Arafah.” 
 Related by Muslim (no. 1162), from Aboo Qataadah (radiyallaahu ’anhu). Related by Muslim (no. 1348), from ’Aa‘ishah (radiyallaahu ’anhaa).  Refer to Jaami’ut-Tirmidhee (3/377).