Today the new year of the Islamic Hijri Calendar has been announced in Makkah. By this determination Thursday the 20th of August 2020 corresponds to 1st Muharram 1442, and the 9th and 10th of Muharram 1442 correspond to Friday 28th and Saturday 29th of August 2020, respectively.
رصد هلال محرم في مرصد تمير ، وغداً بداية العام الجديد 1442 هـ .
— أخبار السعودية (@SaudiNews50) August 19, 2020
Muharram is one of the four sacred months in the Islamic Calendar, and it is generally encouraged to fast throughout this month. The Prophet Muḥammad (sall Allāhu ʿalayhi wa sallam) said:
“The best of fasting after Ramaḍān is fasting during Allāh’s month, Muharram.” 
Allāh stated in the Qur’ān:
“Indeed, the number of months with Allāh is twelve months in the register of Allāh [from] the day He created the heavens and the earth; of these, four are sacred (i.e. 1st, 7th, 11th and 12th months of the Islamic Calendar). That is the correct religion, so do not wrong yourselves during them…” 
The Shar’i Hijri calendar is based on the Islamic tradition of following the sighting of the crescent to declare the end of every lunar month, and the beginning of the next new month. The declaration of the beginning of every Shar’i Hijri month is significant for the Muslims in many ways, including the calculation of Zakah, start and end of Ramadān, declaration of the two ʿEids, calculation of some forms of ʿIddah period, among many other important acts of worship.
Read more: A Reminder about the New Hijri Year
The day of ʿĀshūra’ falls on the 10th of Muharram, ʿĀshūra’ is the day when Allah (subhānahu wa taʿālā) saved Bani Israel (Children of Israel) and Musa (‘alayhi al-Salām) from the Firʿaun (Pharoah). Regarding this day, Ibn ʿAbbās (raḍiy Allāhu ʿanhu) reports:
“The Prophet Muḥammad (sall Allāhu ʿalayhi wa sallam) came to Madīnah and observed that the Jews were fasting on the day of ʿĀshūra’. He asked: ‘What is this?’ They replied: ‘This is a righteous day; it is the day when Allāh saved the Children of Israel from their enemies, so Mūsa fasted on this day.’ He (sall Allāhu ʿalayhi wa sallam) replied: ‘We have more right to Mūsa than you’, so he fasted on that day and commanded the Muslims to do likewise.” 
Read more: The True Significance of ʿĀshūra
In a hugely symbolic act, the Prophet Muḥammad (sall Allāhu ʿalayhi wa sallam) stated his intention to be distinct from other religions by fasting the 9th of Muharram also. ʿAbdullāh b. ʿAbbās (raḍiy Allāhu ʿanhumā), said:
“When the Messenger of Allāh (sall Allāhu ʿalayhi wa sallam) fasted on ʿĀshūra’ and commanded the Muslims to do likewise, they said: ‘O Messenger of Allāh! It is a day that is venerated by the Jews and Christians.’ The Messenger of Allāh (sall Allāhu ʿalayhi wa sallam) replied: ‘If I live to see the next year, inshāAllāh, we will fast on the ninth day, too.’ But it so happened that the Messenger of Allāh (sall Allāhu ʿalayhi wa sallam) passed away before the next year came.’ 
This year, 9th and 10th of Muharram 1442, corresponds to Friday 28th and Saturday 29th of August 2020, respectively.
The Prophet Muḥammad (sall Allāhu ʿalayhi wa sallam) was so keen to observe this fast when he stated: “For fasting the day of ʿĀshūra’, I hope that Allāh will accept it as expiation for the year that went before.” 
 Qur’an 9:36.