Awal Muharram is a national holiday in Malaysia and is celebrated by Muslims as the day symbolises two important events in the Muslim year. Awal means beginning in English and Muharram is the name of the first month in the Muslim calendar.
The day also coincides with the Prophet Muhammad's journey from Mecca to Medina on the first of Muharram in 622AD. Muslims also reflect on the passing of time and their own mortality. To mark the occasion, Muslims attend various religious activities, spiritual singing, religious meetings throughout the country. The marking of the beginning of the new year is usually quiet, unlike New Year's celebrations associated with other calendars.
Muslims gather in mosques for special prayers and readings. They recite Koranic verses and hold special prayers and sermons at public halls and mosques. The New Year itself is known to Muslims as Maal Hijra. In Malaysia, a 'Tokoh Ma'al Hijrah' is awarded to a Muslim personality to honour their contribution to Islam.
Source : http://www.officeholidays.com
Note: The 12 months in Muslim calendar are (in order):
04. Rabi-al-thani / Rabi-al-akhir
06. Jumada-al-thani / Jumada-al-akhir