Although Muharram is a sanctified month as a whole,but the 10th of Muharram is the most sacred of days.This day is called 'ASHORA'.When النَّبِي مُحَمَّدٌ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ migrated to Madina he found that the jews fasted on the 10th Muharram.النَّبِي مُحَمَّدٌ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ has ordered the muslims to fast on the (10th/11th or 9th/10).So as not to immitate the jews.
The best fast besides Ramadaan is the fast of Muharram(Hadith-Muslim).In short it is established in various authentic hadith that fasting on the day of Ashora is a sunnah of النَّبِي مُحَمَّدٌ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ and it makes one entitled to great rewards.
Although the fast is obligatory,to fast on these days is very virtuous."For every fast kept in this month,you get the sawaab of 30days fast".(Tabarani).Fasting on the day of 'ASHORA' all minor sins are forgiven(muslim).Let's try our best to follow the sunnah of our النَّبِي مُحَمَّدٌ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ,and also gain great rewards for our good actions..و عَلَيْكم السَّلاَمُ وَ رَحْمَةُ اللهِ وَبَرَكَاتُهُ وَمَغْفِرَتُهُ وجنته