Islamic New year

The Islamic calendar is based on  a lunar calendar rather than a solar calendar. Which means that each month can be either 29 days long or 30 days long. depending on the sighting of the moon. The first month of the Islamic new year is called Muharram.

Muslims do not celebrate nor congratulate each other on the start of the Islamic New year. However Muslims fast on the 9th and 10th of Muharam. The reason why we fast on these days is  explained in the following article...
Fasting on the day of Ashoora

In order to document  events in Islamic history. The companions of the Prophet peace be upon him decided choose the first year for the Islamic Calendar during the time of Umar's khaliphate.

They chose the first year of the Islamic (Hijri) calendar to be the year in which our beloved Prophet peace be upon him Migrated to the city of Madinah in Present day Saudi Arabia.

The year was a turning point for the Muslims who had suffered persecution for 13 years at the hands of the Non Muslims of Makkah.

They Migrated to Madinah were they were welcomed by the Ansar.  The Prophet peace be upon him on his arrival established a Masjid (Mosque) and later the Islamic State was established in Madinah.
From there the Muslims were able to defend themselves from evil people who wanted to persecute them and kill them simply because they said that "none has the right to be worshiped accept Allah"