In a Sahih Hadith Dhul-Qa'dah, Dhul-Hijjah, Muharram and Rajab are described as sacred months in the Islamic year. In these months reward of virtue is increased by Allah SWT.
there are many virtues described of month of Muharram in Hadiths and also the acts that we should perform to get maximum Ajar. According to Hadith of Sahih Muslim Fasting in Muharram is best after month of Ramadan. Rasool Allah SAW has taught to fast specially on 9th and 10th of Muharram Day of Ashura.
Day of Ashura 10th Muharram also have great significance in Islam history as many important events happened on this day. Fast is kept on Ashura because on this day Moses A.S and his nation got freedom.
we should try to do maximum good deeds in this month. we should stay away from all the Haram acts which some people do in this month by going against Quran and Sunnah.